Deck 1: Functions and Their Graphs

Question 1

Select the graph of the function, and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function.
$g ( x ) = - 2 x \sqrt { 6 - x ^ { 2 } }$

A) The function does not have inverse.
B) The function does not have inverse.
C) The function does not have inverse.
D) The function does not have inverse.
E) The function does not have inverse.

Answer 1

The function does not have inverse.

Question 2

Select the correct graph, showing f and g are inverse functions. $f ( x ) = \frac { x - 1 } { x + 8 } , g ( x ) = - \frac { 8 x + 1 } { x - 1 }$

A)
B)
C)
D)
E)

Answer 2

Question 3

Select the graph of the function, and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function. ​
G(x) = |x + 5| - |x - 5|
​

A)​ The function does not have inverse.
B)​ The function does not have inverse.
C)​ The function does not have inverse.
D)​ The function does not have inverse.
E) The function does not have inverse.

Answer 3

The function does not have inverse.

Question 4

Find the inverse function of f informally.
F(x) = x - 5

A)f^-1(x) = - (x + 5)
B) $f ^ { - 1 } ( x ) = \frac { 5 } { x }$
C) $f ^ { - 1 } ( x ) = \frac { x } { 5 }$
D)f^-1(x) = 5 - x
E)f^-1(x) = x + 5

Question 5

Determine whether the function has an inverse function.If it does, find the inverse function.
$g ( x ) = \frac { x } { 5 }$

A) $g ^ { - 1 } ( x ) = - 5 x$
B) $g ^ { - 1 } ( x ) = 5 x$
C) $g ^ { - 1 } ( x ) = \frac { 5 } { x }$
D) $g ^ { - 1 } ( x ) = - \frac { x } { 5 }$
E)No inverse

Question 6

Select the correct graph, showing f and g are inverse functions.
$f ( x ) = 6 - x ^ { 2 } , g ( x ) = \sqrt { 6 - x } , x \leq 6$

A)
B)
C)
D)
E)

Question 7

Does the function have an inverse function?

Question 8

Select the graph of f and f^-1 on the same set of coordinate axes. ​
F(x) = 2x - 3
​

A)
B)
C)
D)
E)​

Question 9

Select the graph of the function, and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function. $g ( x ) = \frac { 4 - x } { 5 }$

A) The function has an inverse.
B) The function has an inverse.
C) The function has an inverse.
D) The function has an inverse.
E) The function has an inverse.

Question 10

Select the correct graph, showing f and g are inverse functions. $f ( x ) = 9 x , g ( x ) = \frac { x } { 9 }$

A)
B)
C)
D)
E)

Question 11

Select the graph of f and f^-1 on the same set of coordinate axes.
$f ( x ) = \frac { 3 } { x }$

A)
B)
C)
D)
E)

Question 12

Select the correct graph, showing f and g are inverse functions.
$f ( x ) = \frac { x ^ { 3 } } { 7 } , g ( x ) = \sqrt [ 3 ] { 7 x }$

A)
B)
C)
D)
E)

Question 13

Find the inverse function of g(x) = x² - 3 informally.

A) $g ^ { - 1 } ( x ) = \sqrt [ 2 ] { x - 3 }$
B) $g ^ { - 1 } ( x ) = ( x + 3 ) ^ { 2 }$
C) $g ^ { - 1 } ( x ) = x ^ { 2 } + 3$
D) $g ^ { - 1 } ( x ) = \sqrt [ 2 ] { x + 3 }$
E) $g ^ { - 1 } ( x ) = ( x - 3 ) ^ { 2 }$

Question 14

Find the inverse function of f informally.
F(x) = x⁴

A) $f ^ { - 1 } ( x ) = 4 \sqrt { x }$
B) $f ^ { - 1 } ( x ) = \sqrt [ 4 ] { x }$
C) $f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt [ 4 ] { x } }$
D) $f ^ { - 1 } ( x ) = ( \sqrt [ 4 ] { x } ) ^ { 4 }$
E) $f ^ { - 1 } ( x ) = - \sqrt [ 4 ] { x }$

Question 15

Find the inverse function of $f ( x ) = \sqrt { 36 - x ^ { 2 } } , 0 \leq x \leq 6$ .

A) $f ^ { - 1 } ( x ) = \sqrt { 36 - x ^ { 2 } } , 0 \leq x \leq 6$
B) $f ^ { - 1 } ( x ) = \sqrt { x ^ { 2 } - 36 } , 0 \leq x \leq 6$
C) $f ^ { - 1 } ( x ) = 36 - x ^ { 2 } , 0 \leq x \leq 6$
D) $f ^ { - 1 } ( x ) = \sqrt { 36 + x ^ { 2 } } , 0 \leq x \leq 6$
E) $f ^ { - 1 } ( x ) = 36 + x ^ { 2 } , 0 \leq x \leq 6$

Question 16

Select the correct graph, showing f and g are inverse functions. $f ( x ) = 6 x + 1 , g ( x ) = \frac { x - 1 } { 6 }$

A)
B)
C)
D)
E)

Question 17

Determine whether the function has an inverse function.If it does, find the inverse function.
G(x) = x⁷

A) $g ^ { - 1 } ( x ) = \frac { 7 } { x }$
B)g^-1(x) = -7x
C) $g ^ { - 1 } ( x ) = - \frac { x } { 7 }$
D)g^-1(x) = 7x
E)The inverse exists, but none of the above

Question 18

Does the function have an inverse function?

Question 19

Find the inverse function of f informally.
F(x) = 6x

A)f^-1(x) = 6 - x
B)f^-1(x) = 6 + x
C) $f ^ { - 1 } ( x ) = \frac { 1 } { 6 } x$
D)f^-1(x) = x - 6
E)f(x) = 6x

Question 20

Select the correct graph, showing f and g are inverse functions.
$f ( x ) = \sqrt { x - 3 } , g ( x ) = x ^ { 2 } + 3 , x \geq 0$

A)
B)
C)
D)
E)

Question 21

Determine whether the function has an inverse function.If it does, find the inverse function.
F(x) = (x + 4)², x -4

A) $f ^ { - 1 } ( x ) = \sqrt { x } + 4$
B)f^-1(x) = -(x + 4)²
C)f^-1(x) = (x + 4)^-2
D) $f ^ { - 1 } ( x ) = \sqrt { x } - 4$
E)No inverse

Question 22

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f^-1.State the domains and ranges of f and f^-1.

F(x) = -6x² + 2

A) $f ^ { - 1 } ( x ) = \frac { \sqrt { - 6 ( x - 2 ) } } { 6 }$ The domain of f and the range of f^-1 are all real numbers x such that x $\ge$ 0.The domain of f^-1 and the range of f are all real numbers x such that x $\le$ 2.
B) $f ^ { - 1 } ( x ) = \frac { \sqrt { - 2 ( x - 6 ) } } { 2 }$ The domain of f and the range of f^-1 are all real numbers x such that x $\ge$ 0.The domain of f^-1 and the range of f are all real numbers x such that x $\le$ 2.
C) $f ^ { - 1 } ( x ) = \frac { \sqrt { - 6 ( x - 2 ) } } { - 6 }$ The domain of f and the range of f^-1 are all real numbers x such that x $\ge$ 0.The domain of f^-1 and the range of f are all real numbers x such that x $\le$ 2.
D) $f ^ { - 1 } ( x ) = \frac { \sqrt { - 6 ( x - 2 ) } } { 6 }$ The domain of f and the range of f^-1 are all real numbers x such that x $\ge$ 0.The domain of f^-1 and the range of f are all real numbers x such that x $\le$ -2.
E) $f ^ { - 1 } ( x ) = \frac { \sqrt { - 6 ( x + 2 ) } } { 6 }$ The domain of f and the range of f^-1 are all real numbers x such that x $\ge$ 0.The domain of f^-1 and the range of f are all real numbers x such that x $\le$ 2.

Question 23

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f^-1.State the domains and ranges of f and f^-1. ​
F(x) = |x - 9| + 1
​

A)f^-1(x) = x + 8The domain of f and the range of f^-1 are all real numbers x such that x ≥ 9.The domain of f^-1 and the range of f are all real numbers x such that x ≥ 1.
B)f^-1(x) = x - 8The domain of f and the range of f^-1 are all real numbers x such that x ≥ 9.The domain of f^-1 and the range of f are all real numbers x such that x ≥ 1.
C)f^-1(x) = -x - 8The domain of f and the range of f^-1 are all real numbers x such that x ≥ 1.The domain of f^-1 and the range of f are all real numbers x such that x ≥ -9.
D)f^-1(x) = x + 8The domain of f and the range of f^-1 are all real numbers x such that x ≥ -9.The domain of f^-1 and the range of f are all real numbers x such that x ≥ 1.
E)f^-1(x) = -x + 8The domain of f and the range of f^-1 are all real numbers x such that x ≥ 1.The domain of f^-1 and the range of f are all real numbers x such that x ≥ 9.

Question 24

Determine whether the function has an inverse function.If it does, find the inverse function.

F(x) = -2

A)f^-1(x) = 2
B) $f ^ { - 1 } ( x ) = - \frac { 1 } { 2 }$
C) $f ^ { - 1 } ( x ) = \frac { 1 } { 2 }$
D)f^-1(x) = -2
E)No inverse

Question 25

Use the functions given by $f ( x ) = \frac { 1 } { 8 } x - 5$ and g(x) = x³ to find (g^-1 _º f^-1)(-5).

A)-2
B)0
C)-4
D)2
E)4

Question 26

Restrict the domain of f(x) = x² + 5 to x ≥ 0.Use a graphing utility to graph the function. ​

A)​
B)
C)​
D)​
E)

Question 27

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f^-1.State the domains and ranges of f and f^-1.

F(x) = (x - 5)²

A) $f ^ { - 1 } ( x ) = \sqrt { x } - 5$
The domain of f and the range of f^-1 are all real numbers x such that x $\ge$ 5.The domain of f^-1 and the range of f are all real numbers x such that x $\ge$ 0.
B) $f ^ { - 1 } ( x ) = \sqrt { x } + 5$
The domain of f and the range of f^-1 are all real numbers x such that x $\ge$ 0.The domain of f^-1 and the range of f are all real numbers x such that x $\ge$ -5.
C) $f ^ { - 1 } ( x ) = \sqrt { x } + 5$
The domain of f and the range of f^-1 are all real numbers x such that x $\ge$ 5.The domain of f^-1 and the range of f are all real numbers x such that x $\ge$ 0.
D) $f ^ { - 1 } ( x ) = \sqrt { x } + 5$
The domain of f and the range of f^-1 are all real numbers x such that x $\ge$ 0.The domain of f^-1 and the range of f are all real numbers x such that x $\ge$ 5.
E) $f ^ { - 1 } ( x ) = \sqrt { x } - 5$
The domain of f and the range of f^-1 are all real numbers x such that x $\ge$ -5.The domain of f^-1 and the range of f are all real numbers x such that x $\ge$ 0.

Question 28

Restrict the domain of the function f so that the function is one-to-one and has an inverse function.Then find the inverse function f^-1.State the domains and ranges of f and f^-1. ​
F(x) = |x + 5|
​

A)f​^-1(x) = x - 5​The domain of f and the range of f^-1 are all real numbers x such that x ≥ -5.The domain of f^-1 and the range of f are all real numbers x such that x ≥ 0.
B)f​^-1(x) = x + 5​The domain of f and the range of f^-1 are all real numbers x such that x ≥ 0.The domain of f^-1 and the range of f are all real numbers x such that x ≥ -5.
C)f​^-1(x) = x - 5​The domain of f and the range of f^-1 are all real numbers x such that x ≥ 0.The domain of f^-1 and the range of f are all real numbers x such that x ≥ 5.
D)f​^-1(x) = x + 5​The domain of f and the range of f^-1 are all real numbers x such that x ≥ 5.The domain of f^-1 and the range of f are all real numbers x such that x ≥ 0.
E)f​^-1(x) = x - 5​The domain of f and the range of f^-1 are all real numbers x such that x ≥ 5.The domain of f^-1 and the range of f are all real numbers x such that x ≥ 0.

Question 29

Use the functions given by $f ( x ) = \frac { 1 } { 8 } x - 1$ and g(x) = x³ to find (f^-1 _º g^-1)(1).

A)14
B)12
C)16
D)20
E)18

Question 30

Use the functions given by $f ( x ) = \frac { 1 } { 125 } x - 1$ and g(x) = x³ to find (f _º g)^-1.

A) $5 \sqrt [ 3 ] { x - 1 }$
B) $125 \sqrt [ 3 ] { x - 1 }$
C) $5 \sqrt [ 3 ] { x + 1 }$
D) $125 \sqrt [ 3 ] { x + 1 }$
E) $5 \sqrt { x + 1 }$

Question 31

The function given by y = 0.03x² + 245.50, 0 < x < 100 approximates the exhaust temperature y in degrees Fahrenheit, x where is the percent load for a diesel engine.Find the inverse function.

A) $y = \frac { x + 245.50 } { - 0.03 }$
B) $y = \sqrt { \frac { x - 245.50 } { 0.03 } }$
C) $y = \frac { x - 245.50 } { 0.03 }$
D) $y = \sqrt { \frac { x + 245.50 } { 0.03 } }$
E) $y = \frac { x + 245.50 } { 0.03 }$

Question 32

Use the functions given by f(x) = x + 2 and g(x) = 2x - 5 to find (f _º g)^-1.

A) $\frac { x + 3 } { 2 }$
B) $\frac { x - 3 } { - 2 }$
C) $\frac { x - 4 } { 3 }$
D) $\frac { x - 3 } { 2 }$
E) $\frac { - x - 3 } { 2 }$

Question 33

Your wage is $11.00 per hour plus $0.50 for each unit produced per hour.So, your hourly wage in terms of the number of units produced x is y = 11 + 0.50x.Find the inverse function.What does each variable represent in the inverse function

A) $y = \frac { x - 11 } { 0.50 }$ x = hourly wage; y = numbers of units produced
B)y = 11 + 0.50xx = hourly wage; y = numbers of units produced
C) $y = \frac { x + 11 } { 0.50 }$ x = hourly wage; y = numbers of units produced
D) $y = \frac { 11 - x } { 0.50 }$ x = hourly wage; y = numbers of units produced
E)y = 11 - 0.50xx = hourly wage; y = numbers of units produced

Question 34

Determine whether the function has an inverse function.If it does, find the inverse function.
$f ( x ) = \left\{ \begin{array} { l } x + 2 , x < 0 \\2 - x , x \geq 0\end{array} \right.$

A) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 2 + x , x \geq 0 \\x - 2 , x < 0\end{array} \right.$
B) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 2 + x , x \geq 0 \\x - 2 , x < 0\end{array} \right.$ .
C) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } x - 2 , x \geq 0 \\2 + x , x < 0\end{array} \right.$
D) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } x + 2 , x \geq 0 \\2 - x , x < 0\end{array} \right.$
E)No inverse

Question 35

Use the graph of the function f to create a table of values for the given points.Then create a second table that can be used to find f^-1.

A)
$\begin{array}{|l|l|l|l|l|}\hline x & 1 & 4 & 7 & 8 \\\hline y & 1 & 4 & 7 & 9 \\\hline\end{array}$

$\begin{array}{|l|l|l|l|l|}\hline x & 1 & 4 & 7 & 9 \\\hline f^{-1}(x) & 1 & 4 & 7 & 8 \\\hline\end{array}$
B)
$\begin{array}{|l|l|l|l|l|}\hline x & 1 & 4 & 7 & 9 \\\hline y & 1 & 4 & 7 & 8 \\\hline\end{array}$

$\begin{array}{|l|l|l|l|l|}\hline x & 1 & 4 & 7 & 8 \\\hline f^{-1}(x) & 1 & 4 & 7 & 9 \\\hline\end{array}$
C)
$\begin{array}{l}\begin{array} { | l | l | l | l | l | } \hline x & 1 & 4 & 7 & 8 \\\hline y & 1 & 4 & 7 & 9 \\\hline\end{array}\\\\\begin{array} { | l | l | l | l | l | } \hline x & 1 & 4 & 7 & 9 \\\hline f ^ { - 1 } ( x ) & - 1 & - 4 & - 7 & - 8 \\\hline\end{array}\end{array}$
D)
$\begin{array}{l}\begin{array} { | l | l | l | l | l | } \hline x & - 1 & - 4 & - 7 & - 9 \\\hline y & 1 & 4 & 7 & 8 \\\hline\end{array}\\\\\begin{array} { | l | l | l | l | l | } \hline x & 1 & 4 & 7 & 8 \\\hline f ^ { - 1 } ( x ) & 1 & 4 & 7 & 9 \\\hline\end{array}\end{array}$
E)
$\begin{array}{l}\begin{array} { | l | l | l | l | l | } \hline x & - 1 & - 4 & - 7 & - 9 \\\hline y & 1 & 4 & 7 & 8 \\\hline\end{array}\\\\\begin{array} { | l | l | l | l | l | } \hline x & 1 & 4 & 7 & 9 \\\hline f ^ { - 1 } ( x ) & - 1 & - 4 & - 7 & - 8 \\\hline\end{array}\end{array}$

Question 36

Determine whether the function has an inverse function.If it does, find the inverse function.
$h ( x ) = - \frac { 4 } { x ^ { 2 } }$

A) $h ^ { - 1 } ( x ) = \frac { 4 } { x ^ { 2 } }$
B) $h ^ { - 1 } ( x ) = - \frac { x ^ { 2 } } { 4 }$
C) $h ^ { - 1 } ( x ) = - \frac { 4 } { x ^ { 2 } }$
D) $h ^ { - 1 } ( x ) = \frac { x ^ { 2 } } { 4 }$
E)No inverse

Question 37

Use the functions given by $f ( x ) = \frac { 1 } { 8 } x - 5$ and g(x) = x³ to find (f^-1 _º f^-1)(-5).

A)36
B)44
C)40
D)38
E)42

Question 38

Use the functions given by f(x) = x + 6 and g(x) = 7x - 3 to find g^-1 _º f^-1.

A) $\frac { - x - 3 } { 7 }$
B) $\frac { x + 3 } { 7 }$
C) $\frac { x - 3 } { 7 }$
D) $\frac { x - 3 } { - 7 }$
E) $\frac { x - 7 } { 3 }$

Question 39

Use the functions given by $f ( x ) = \frac { 1 } { 64 } x - 4$ and g(x) = x³ to find g^-1 _º f^-1.

A) $4 \sqrt [ 3 ] { ( 4 - x ) }$
B) $- 4 \sqrt [ 3 ] { ( x + 4 ) }$
C) $- 4 \sqrt [ 3 ] { ( x - 4 ) }$
D) $4 \sqrt [ 3 ] { ( x - 4 ) }$
E) $4 \sqrt [ 3 ] { ( x + 4 ) }$

Question 40

Determine whether the function has an inverse function.If it does, find the inverse function.
$f ( x ) = \sqrt { 7 x + 8 }$

A) $f ^ { - 1 } ( x ) = - \frac { x ^ { 2 } + 8 } { 7 }$
B) $f ^ { - 1 } ( x ) = - \frac { x ^ { 2 } - 8 } { 7 }$
C) $f ^ { - 1 } ( x ) = \frac { x ^ { 2 } - 8 } { 7 }$
D) $f ^ { - 1 } ( x ) = \frac { x ^ { 2 } + 8 } { 7 }$
E)No Inverse

Question 41

Find the inverse of the one-to-one function.
​
y = 5x + 4
​
f ^-1(x) = __________

Question 42

Find the inverse of the one-to-one function. $y = \frac { 1 } { 8 x }$

A) $f ^ { - 1 } ( x ) = \frac { 8 } { x }$
B) $f ^ { - 1 } ( x ) = \frac { x } { 8 }$
C) $f ^ { - 1 } ( x ) = 8 x$
D) $f ^ { - 1 } ( x ) = \frac { 1 } { 8 x }$
E)inverse does not exist

Question 43

Determine algebraically whether f and g are inverse functions. f(x) = 5x - 3 $g ( x ) = \frac { x + 3 } { 5 }$

A)Yes, f and g are inverse functions. $$f ( g ( x ) ) = f \left( \frac { x + 3 } { 5 } \right) = 5 \left( \frac { x + 3 } { 5 } \right) - 3 = x + 3 - 3 = x$$ $$g ( f ( x ) ) = g ( 5 x - 3 ) = \frac { 5 x - 3 + 3 } { 5 } = \frac { 5 x } { 5 } = x$$
B)No, f and g are not inverse functions. $$f ( g ( x ) ) = f \left( \frac { x + 3 } { 5 } \right) = 5 \left( \frac { x + 3 } { 5 } \right) - 3 = x + 3 - 3 = x$$ $$g ( f ( x ) ) = g ( 5 x - 3 ) = \frac { 5 x - 3 + 3 } { 5 } = \frac { 5 x } { 5 } = - x$$

Question 44

Graph the given function. f(x) = (x - 3)²

A)
B)
C)
D)
E)

Question 45

Determine whether the function has an inverse function.If it does, find the inverse function. $$f ( x ) = \left\{ \begin{array} { l } 8 x + 13 , x < - 2 \\( x + 2 ) ^ { 2 } - 3 , x \geq - 2\end{array} \right.$$

A) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } \frac { x - 13 } { 8 } , x < - 2 \\\sqrt { x + 3 } - 2 , x \geq - 2\end{array} \right.$
B) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { c } \frac { x - 13 } { 8 } , x < - 2 \\\sqrt { x + 1 } , x \geq - 2\end{array} \right.$
C) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } \frac { x - 13 } { 8 } , x < - 3 \\\sqrt { x + 3 } - 2 , x \geq - 3\end{array} \right.$
D) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } \frac { x + 13 } { 8 } , x < - 3 \\\sqrt { x + 3 } - 2 , x \geq - 3\end{array} \right.$
E)No inverse function exists.

Question 46

The function f(x) = x² - 2 is one-to-one on the domain (x $\le$ 0) .Find f ^-1(x).

A) $f ^ { - 1 } ( x ) = - \sqrt { x + 2 }$
B) $f ^ { - 1 } ( x ) = \frac { 1 } { x ^ { 2 } - 2 }$
C) $f ^ { - 1 } ( x ) = \sqrt { x + 2 }$
D) $f ^ { - 1 } ( x ) = \sqrt { x - 2 }$
E)f ^-1(x) = x² + 2

Question 47

Find (f + g)(x). $f ( x ) = x + 4 , g ( x ) = x - 4$

A)2x
B)4x
C)-4x
D)-2x
E)2x + 8

Question 48

Find (f + g)(x). $f ( x ) = 2 x - 3 , g ( x ) = 4 - x$

A) $3 x - 1$
B) $2 x - 1$
C) $2 x + 1$
D) $3 x + 1$
E) $x + 1$

Question 49

Determine whether the function is one-to- one. ​
Y = 3x
​

A)No, it isn't one-to-one.
B)Yes, it is one-to-one.

Question 50

Find (f - g)(x). $f ( x ) = 2 x - 2 , g ( x ) = 4 - x$

A) $3 x - 6$
B) $2 x + 6$
C) $2 x - 6$
D) $x - 6$
E) $3 x + 6$

Question 51

Determine whether the function has an inverse function.If it does, find the inverse function. f(x) = x² + 5

A) $f ^ { - 1 } ( x ) = \sqrt { x } + 5 , x \geq 0$
B) $f ^ { - 1 } ( x ) = \sqrt { x - 5 }$
C) $f ^ { - 1 } ( x ) = \sqrt { x } - 5$
D) $f ^ { - 1 } ( x ) = \sqrt { x + 5 } , x \geq - 5$
E)No inverse function exists.

Question 52

Find the inverse of the one-to-one function.

Y = 3x

A) $f ^ { - 1 } ( x ) = 3 x ^ { 2 }$
B)f ^-1(x) = 3x
C) $f ^ { - 1 } ( x ) = \frac { x } { 3 }$
D) $f ^ { - 1 } ( x ) = \frac { 3 } { x }$
E)f ^-1(x) = 9x

Question 53

Use the functions given by $f ( x ) = \frac { x } { 8 } - 1$ and g(x) = x³ to find the indicated value. (f _º g)^-1(5)

A) $- \frac { 387 } { 512 }$
B) $2 \sqrt [ 3 ] { 6 }$
C) $- 2 \sqrt [ 3 ] { 6 }$
D) $2 \sqrt [ 3 ] { 4 }$
E) Undefined

Question 54

Find (f - g)(x). $f ( x ) = x + 3 , g ( x ) = x - 3$

A)2x - 6
B)6
C)2x - 3
D)2x + 6
E)2x

Question 55

Find the inverse of the one-to-one function.

Y = 5x + 9

A) $f ^ { - 1 } ( x ) = \frac { x + 9 } { 5 }$
B) $f ^ { - 1 } ( x ) = \frac { x - 9 } { 5 }$
C) $f ^ { - 1 } ( x ) = \frac { 5 } { x - 9 }$
D) $f ^ { - 1 } ( x ) = \frac { x - 5 } { 9 }$
E)none of the above

Question 56

Find the inverse of the one-to-one function.
​
y = 6x
​
f ^-1(x) = __________

Question 57

Determine algebraically whether f and g are inverse functions. $f ( x ) = \sqrt { x + 6 }$ g(x) = x² - 6, x $\ge$ 0

Question 58

Find the inverse of the one-to-one function.
​ ​
f ^-1(x) = __________

Question 59

Show algebraically that f and g are inverse functions.
f(x) = 9x + 9

Question 60

Determine whether the function is one-to-one. ​
Y = (x - 5)²; x ≥ 5
​

A)No, it isn't one-to-one.
B)Yes, it is one-to-one.

Question 61

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 5$ and $g ( x ) = x - 4$ . $( f / g ) ( 5 )$

A)30
B) $\frac { 5 } { 34 }$
C) $\frac { 32 } { 3 }$
D) $\frac { 2 } { 31 }$
E) $\frac { 34 } { 5 }$

Question 62

Find $f \circ g$ and the domain of the composite function.
$f ( x ) = | x | , g ( x ) = x + 3$

A) $\left| ( x - 3 ) ^ { 3 } \right|$ Domain of $f \circ g$ : all real numbers x
B) $\sqrt { ( x + 3 ) ^ { 3 } }$ Domain of $f \circ g$ : all real numbers x
C) $| x + 3 |$ Domain of $f \circ g$ : all real numbers x
D) $\left| ( x + 3 ) ^ { 3 } \right|$ Domain of $f \circ g$ : all real numbers x
E) $| x - 3 |$ Domain of $f \circ g$ : all real numbers x

Question 63

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 3$ and $g ( x ) = x - 4$ . $( f - g ) ( 3 t )$

A) $9 t ^ { 2 } + 3 t + 7$
B) $6 t + 7$
C) $9 t ^ { 2 } + 3 t - 7$
D) $9 t ^ { 2 } - 3 t - 7$
E) $9 t ^ { 2 } - 3 t + 7$

Question 64

Find $g \circ f$ .
$f ( x ) = x ^ { 2 } , g ( x ) = x - 4$

A) $x ^ { 2 } - 4$
B) $x ^ { 2 }$
C) $( x - 4 ) ^ { 2 }$
D) $\left( x ^ { 2 } + 4 \right)$
E) $( x + 4 ) ^ { 2 }$

Question 65

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 2$ and $g ( x ) = x - 6$ . $( f - g ) ( - 5 )$

A)28
B)38
C)-38
D)125
E)17

Question 66

Find $g \circ g$ .
$g ( x ) = x - 2$

A) $( x - 2 ) ^ { 2 }$
B) $x ^ { 2 } - 2$
C) $x + 4$
D) $- x - 4$
E) $x - 4$

Question 67

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 5$ and $g ( x ) = x - 2$ . $( f g ) ( 5 )$

A)92
B)90
C)-86
D)89
E)91

Question 68

Find $( f / g ) ( x )$ . $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = \frac { 1 } { x ^ { 4 } }$

A) $\frac { 1 } { x ^ { 2 } }$
B) $x ^ { 6 }$
C) $\frac { 1 } { x ^ { 4 } }$
D) $\frac { 1 } { x ^ { 6 } }$
E) $x ^ { 2 }$

Question 69

Find (f + g)(x). $f ( x ) = x ^ { 2 } + 4 , g ( x ) = \sqrt { 7 - x }$

A) $x ^ { 2 } + 4 - \sqrt { 7 - x }$
B) $x ^ { 2 } + 4 + \sqrt { 7 - x }$
C) $x ^ { 2 } - 4 + \sqrt { 7 + x }$
D) $x ^ { 2 } - 4 - \sqrt { 7 - x }$
E) $x ^ { 2 } - 4 + \sqrt { 7 - x }$

Question 70

Find $( f g ) ( x )$ . $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = \frac { 1 } { x ^ { 4 } }$

A) $\frac { 1 } { x ^ { 4 } }$
B) $\frac { 1 } { x ^ { 2 } }$
C) $\frac { 1 } { x ^ { 6 } }$
D) $x ^ { 6 }$
E) $\frac { x ^ { 4 } } { x ^ { 2 } }$

Question 71

Find $f \circ g$ and the domain of the composite function.
$f ( x ) = \sqrt { x + 5 } , g ( x ) = x ^ { 2 }$

A) $( x + 5 ) ^ { 2 }$ Domain of $f \circ g$ : all real numbers x
B) $\sqrt { x ^ { 2 } + 5 }$ Domain of $f \circ g$ : all real numbers x
C) $- \sqrt { ( x + 5 ) ^ { 2 } }$ Domain of $f \circ g$ : all real numbers x
D) $( x - 5 ) ^ { 2 }$ Domain of $f \circ g$ : all real numbers x
E) $\sqrt { ( x - 5 ) ^ { 2 } }$ Domain of $f \circ g$ : all real numbers x

Question 72

Find (f / g)(x).What is the domain of f / g
$f ( x ) = x ^ { 2 } , g ( x ) = 7 x - 3$

A) $- \frac { x ^ { 2 } } { 7 x - 3 }$ ; all real numbers x.
B) $\frac { 7 x + 3 } { x ^ { 2 } }$ ; all real numbers x except x = 0
C) $\frac { x ^ { 2 } } { 7 x - 3 }$ ; all real numbers x except x = $\frac { 3 } { 7 }$
D) $\frac { 7 x - 3 } { x ^ { 2 } }$ ; all real numbers x except x = 0
E) $\frac { x ^ { 2 } } { 7 x + 3 }$ ; all real numbers x except x = $\frac { 7 } { 3 }$

Question 73

Find (fg)(x). $f ( x ) = x ^ { 2 } , g ( x ) = 7 x - 7$

A) $7 x ^ { 3 } + 7 x ^ { 2 }$
B) $7 x ^ { 3 } - 7 x ^ { 2 }$
C) $7 x ^ { 2 } - 7 x ^ { 3 }$
D) $7 x ^ { 2 } + 7 x ^ { 3 }$
E) $7 x - 7 x ^ { 2 }$

Question 74

Find $f \circ g$ .
$f ( x ) = x ^ { 2 } , g ( x ) = x - 2$

A) $x ^ { 2 }$
B) $( x - 2 ) ^ { 2 }$
C) $( x + 2 ) ^ { 2 }$
D) $\left( x ^ { 2 } - 2 \right)$
E) $\left( x ^ { 2 } + 2 \right)$

Question 75

Find $g \circ f$ and the domain of the composite function.
$f ( x ) = x ^ { 2 } + 4 , g ( x ) = \sqrt { x }$

A) $( x + 4 ) ^ { 4 }$ Domain of $g \circ f$ : all real numbers x
B) $( x - 4 ) ^ { 4 }$ Domain of $g \circ f$ : all real numbers x
C) $\sqrt { x ^ { 2 } + 4 }$ Domain of $g \circ f$ : all real numbers x
D) $\sqrt { ( x - 4 ) ^ { 4 } }$ Domain of $g \circ f$ : all real numbers x
E) $\sqrt { ( x + 4 ) ^ { 4 } }$ Domain of $g \circ f$ : all real numbers x

Question 76

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 6$ and $g ( x ) = x - 5$ . $( f / g ) ( - 4 ) - g ( 6 )$

A) $- \frac { 5 } { 26 }$
B) $- \frac { 31 } { 9 }$
C) $- \frac { 9 } { 13 }$
D) $- \frac { 13 } { 9 }$
E) $- \frac { 9 } { 31 }$

Question 77

Find $( f - g ) ( x )$ . $f ( x ) = x ^ { 2 } + 3 , g ( x ) = \sqrt { 5 - x }$

A) $x ^ { 2 } + 3 + \sqrt { 5 - x }$
B) $x ^ { 2 } - 3 + \sqrt { 5 - x }$
C) $x ^ { 2 } - 3 + \sqrt { 5 + x }$
D) $x ^ { 2 } + 3 - \sqrt { 5 - x }$
E) $x ^ { 2 } - 3 - \sqrt { 5 - x }$

Question 78

Find $g \circ f$ and the domain of the composite function.
$f ( x ) = | x | , g ( x ) = x + 4$

A) $| x - 4 |$ Domain of $g \circ f$ : all real numbers x
B) $x - | 4 |$ Domain of $g \circ f$ : all real numbers x
C) $| x | - 4$ Domain of $g \circ f$ : all real numbers x
D) $| x | + 4$ Domain of $g \circ f$ : all real numbers x
E) $| x + 4 |$ Domain of $g \circ f$ : all real numbers x

Question 79

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 2$ and $g ( x ) = x - 4$ . $( f + g ) ( 3 )$

A)12
B)-10
C)7
D)14
E)10

Question 80

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 3$ and $g ( x ) = x - 6$ . $( f - g ) ( 0 )$

A)48
B)39
C)9
D)0
E)-39