Question 1

Find the indicated function value.
-$$f ( x ) = 4 x + 5 , g ( x ) = - 4 x + 3$$
Find $( f + g ) ( - 1 )$.
A) 8
B) $- 6$
C) 5
D) 4

Accepted Answer

The answer of Find the indicated function value.
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Question 2

For the pair of functions, determine the domain of f + g.
-$$f ( x ) = 5 x - 1 , g ( x ) = \frac { 4 } { x - 2 }$$
A) $( \infty , \infty )$
B) $( 0 , \infty )$
C) $( x , - 4 )$ or $( - 4 , \infty )$
D) $( \infty , 2 )$ or $( 2 , \infty )$

Accepted Answer

The domain of $f(x) = 5x - 1$ is all real numbers, but the domain of $g(x) = \frac{4}{x - 2}$ excludes $x = 2$ because division by zero is undefined. Therefore, the domain of $f + g$ is all real numbers except $x = 2$, which corresponds to $(-\infty, 2)$ and $(2, \infty)$.

Question 3

Find the indicated function value.
-$$f ( x ) = 3 x - 1 , g ( x ) = 2 x ^ { 2 } - 1$$
Find $( f + g ) ( 3 )$.
A) 26
B) 27
C) 25
D) 19

Accepted Answer

The answer of Find the indicated function value.
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Question 4

Find the domain of the function.
-$$f ( x ) = \frac { 1 } { x - 5 } + \frac { 4 } { x + 10 }$$
A) $( \infty , - 5 )$ or $( - 5,10 )$ or $( 10 , \infty )$
B) $( \infty , - 10 )$ or $( - 10,5 )$ or $( 5 , \infty )$
C) $( \infty , \infty )$
D) $( \infty , - 10 )$ or $( 5 , \infty )$

Accepted Answer

The domain of the function excludes values that make the denominator zero. For $f(x) = \frac{1}{x-5} + \frac{4}{x+10}$, the denominators $x-5$ and $x+10$ cannot be zero, so $x \neq 5$ and $x \neq -10$. Thus, the domain is all real numbers except 5 and -10, which matches choice B.

Question 5

Find the domain of the function.
-$$f ( x ) = x - \frac { 7 } { x - 3 }$$
A) $( \infty , 7 )$ or $( 7 , \infty )$
B) $( \infty , \infty )$
C) $( \infty , 0 )$ or $( 0 , \infty )$
D) $( \infty , 3 )$ or $( 3 , \infty )$

Accepted Answer

The domain of the function excludes values that make the denominator zero. Since the denominator is $x - 3$, setting it equal to zero gives $x = 3$. Therefore, the domain is all real numbers except $x = 3$, which is represented by $(-\infty, 3)$ and $(3, \infty)$.

Question 6

Find the domain of the function.
-$$f ( x ) = \frac { x } { x ^ { 2 } + 8 }$$
A) $( \infty , - 8 )$ or $( - 8 , \infty )$
B) $( \infty , 0 )$ or $( 0 , \infty )$
C) $( - 8 , \infty )$
D) $( \infty , \infty )$

Accepted Answer

The domain of the function $f(x) = \frac{x}{x^2 + 8}$ is all real numbers because the denominator $x^2 + 8$ is never zero (since $x^2$ is always non-negative, $x^2 + 8$ is always positive). Therefore, the function is defined for all real numbers.

Question 7

For the pair of functions, determine the domain of f + g.
-$$f ( x ) = 3 x ^ { 2 } + 1 , g ( x ) = 5 x ^ { 3 } - 7$$
A) $( \infty , \infty )$
B) $( \infty , 0 )$
C) $( 0 , \infty )$
D) $( \infty , 0 )$ or $( 0 , \infty )$

Accepted Answer

The domain of both $f(x) = 3x^2 + 1$ and $g(x) = 5x^3 - 7$ is all real numbers, since there are no restrictions on $x$ for polynomials. Therefore, the domain of $f + g$ is also all real numbers, which is represented as $(-\infty, \infty)$.

Question 8

For the pair of functions, determine the domain of f + g.
-$$f ( x ) = \frac { 2 x } { x - 1 } , g ( x ) = \frac { 4 } { x + 9 }$$
A) $( \infty , \infty )$
B) $( \infty , - 9 )$ or $( 1 , \infty )$
C) $( \infty , - 1 )$ or $( - 1,9 )$ or $( 9 , \infty )$
D) $( - \infty , - 9 )$ or $( - 9,1 )$ or $( 1 , \infty )$

Accepted Answer

The domain of $f + g$ is determined by the values of $x$ for which both $f(x)$ and $g(x)$ are defined. For $f(x) = \frac{2x}{x-1}$, $x$ cannot be 1 because the denominator would be 0. For $g(x) = \frac{4}{x+9}$, $x$ cannot be -9 for the same reason. Therefore, the domain of $f + g$ excludes -9 and 1, making the correct domain $( - \infty , - 9 )$ or $( - 9,1 )$ or $( 1 , \infty )$.

Question 9

Find the requested value.
-$$f ( x ) = - 5 x ^ { 2 } - 5 x + 8 , g ( x ) = 3 x - 8$$
Find $f ( - 2 ) + g ( - 2 )$.
A) 24
B) 2
C) 26
D) $- 16$

Accepted Answer

The answer of Find the requested value.
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Question 10

For the pair of functions, determine the domain of f + g.
-$$f ( x ) = 5 x + 5 , g ( x ) = \frac { 3 } { x + 1 }$$
A) $( \infty , \infty )$
B) $( 0 , \infty )$
C) $( \infty , - 3 )$ or $( - 3 , \infty )$
D) $( - , - 1 )$ or $( - 1 , \infty )$

Accepted Answer

The domain of $f(x) = 5x + 5$ is all real numbers, but the domain of $g(x) = \frac{3}{x+1}$ excludes $x = -1$ because the denominator cannot be zero. Therefore, the domain of $f + g$ is all real numbers except $x = -1$, which is option D.

Question 11

Find the domain of the function.
-$$f ( x ) = \frac { - 5 x } { x + 3 }$$
A) $( \infty , - 3 )$ or $( - 3 , \infty )$
B) $( \infty , \infty )$
C) $( - , - 3 )$
D) $( x , 0 )$ or $( 0 , \infty )$

Accepted Answer

The domain of the function excludes the value for which the denominator is zero, which is $x = -3$. Therefore, the domain is all real numbers except $x = -3$, represented as $(-\infty, -3)$ union $(-3, \infty)$.

Question 12

Find the indicated function value.
-$$f ( x ) = 2 x ^ { 2 } - 2 , g ( x ) = 3 x ^ { 2 } + 3 x - 3$$
Find $( f + g ) ( 4 )$.
A) 63
B) 93
C) 51
D) 87

Accepted Answer

The answer of Find the indicated function value.
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Question 13

Find the indicated function value.
-$$f ( x ) = 9 - 7 x , g ( x ) = - 3 x + 7$$
Find $( f + g ) ( x )$.
A) $- 10 x + 16$
B) $6 x$
C) $- 3 x + 9$
D) $- 4 x + 16$

Accepted Answer

To find $(f + g)(x)$, you add the functions $f(x)$ and $g(x)$ together: $f(x) + g(x) = (9 - 7x) + (-3x + 7) = 9 - 7x - 3x + 7 = -10x + 16$.

Question 14

Find the requested value.
-$$f ( x ) = - 3 x ^ { 2 } - 4 , g ( x ) = x - 1$$
Find $f ( - 4 ) - g ( - 4 )$.
A) $- 47$
B) 56
C) $- 55$
D) $- 49$

Accepted Answer

The answer of Find the requested value.
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Question 15

Find the indicated function value.
-$$f ( x ) = 2 x - 5 , g ( x ) = 2 x ^ { 2 } + 2 x - 1$$
Find $( f + g ) ( 4 )$.
A) 42
B) 26
C) 34
D) 36

Accepted Answer

The answer of Find the indicated function value.
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Question 16

Find the indicated function value.
-$$f ( x ) = x ^ { 2 } + \frac { 1 } { 3 } x - 3 , g ( x ) = x ^ { 3 } - \frac { 2 } { 3 } x ^ { 2 } + x$$
Find $( f + g ) ( x )$.
A) $x ^ { 3 } + \frac { 1 } { 3 } x ^ { 2 } + \frac { 4 } { 3 } x - 3$
B) $2 x ^ { 3 } - \frac { 1 } { 6 } x ^ { 2 } - 2 x$
C) $x ^ { 3 } + \frac { 1 } { 6 } x ^ { 2 } + \frac { 2 } { 3 } x - 3$
D) $2 x ^ { 3 } - \frac { 1 } { 3 } x ^ { 2 } - 2 x$

Accepted Answer

To find $(f + g)(x)$, add the corresponding terms of $f(x)$ and $g(x)$: $x^2 + \frac{1}{3}x - 3 + x^3 - \frac{2}{3}x^2 + x = x^3 + \left(1 - \frac{2}{3}\right)x^2 + \left(\frac{1}{3} + 1\right)x - 3 = x^3 + \frac{1}{3}x^2 + \frac{4}{3}x - 3$.

Question 17

Find the indicated function value.
-$$f ( x ) = 4 x ^ { 2 } - 4 , g ( x ) = 2 x ^ { 2 } - 2$$
Find $( f + g ) ( 5 )$.
A) 148
B) 48
C) 144
D) 104

Accepted Answer

The answer of Find the indicated function value.
-\[f ( x...

Question 18

Find the domain of the function.
-$$f ( x ) = x ^ { 2 } + 8$$
A) $[ - 8 , \infty )$
B) $( \infty , - 8 )$ or $( - 8 , \infty )$
C) $( - 8 , \infty )$
D) $( \infty , \infty )$

Accepted Answer

The domain of a quadratic function like $f(x) = x^2 + 8$ is all real numbers, because you can plug any real number into the function and get a valid output. The notation $(-\infty, \infty)$ represents all real numbers.

Question 19

Find the indicated function value.
-$$f ( x ) = x + 2 , g ( x ) = x + 7$$
Find $( f + g ) ( 1 )$.
A) 11
B) $- 7$
C) 7
D) $- 3$

Accepted Answer

The sum of functions $f$ and $g$ evaluated at $x = 1$ is $(f + g)(1) = f(1) + g(1) = (1 + 2) + (1 + 7) = 3 + 8 = 11.$

Question 20

Find the indicated function value.
-$$f ( x ) = 5 x ^ { 2 } + 7 x + 6 , g ( x ) = 3 x + 4$$
Find $( f + g ) ( 5 )$.
A) 245
B) 261
C) 185
D) $- 65$

Accepted Answer

The answer of Find the indicated function value.
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Quiz 2: Functions and Linear Functions

Find the indicated function value. - $f ( x ) = 4 x + 5 , g ( x ) = - 4 x + 3$ Find $( f + g ) ( - 1 )$ .

For the pair of functions, determine the domain of f + g. - $f ( x ) = 5 x - 1 , g ( x ) = \frac { 4 } { x - 2 }$

Find the indicated function value. - $f ( x ) = 3 x - 1 , g ( x ) = 2 x ^ { 2 } - 1$ Find $( f + g ) ( 3 )$ .

Find the domain of the function. - $f ( x ) = \frac { 1 } { x - 5 } + \frac { 4 } { x + 10 }$

Find the domain of the function. - $f ( x ) = x - \frac { 7 } { x - 3 }$

Find the domain of the function. - $f ( x ) = \frac { x } { x ^ { 2 } + 8 }$

For the pair of functions, determine the domain of f + g. - $f ( x ) = 3 x ^ { 2 } + 1 , g ( x ) = 5 x ^ { 3 } - 7$

For the pair of functions, determine the domain of f + g. - $f ( x ) = \frac { 2 x } { x - 1 } , g ( x ) = \frac { 4 } { x + 9 }$

Find the requested value. - $f ( x ) = - 5 x ^ { 2 } - 5 x + 8 , g ( x ) = 3 x - 8$ Find $f ( - 2 ) + g ( - 2 )$ .

For the pair of functions, determine the domain of f + g. - $f ( x ) = 5 x + 5 , g ( x ) = \frac { 3 } { x + 1 }$

Find the domain of the function. - $f ( x ) = \frac { - 5 x } { x + 3 }$

Find the indicated function value. - $f ( x ) = 2 x ^ { 2 } - 2 , g ( x ) = 3 x ^ { 2 } + 3 x - 3$ Find $( f + g ) ( 4 )$ .

Find the indicated function value. - $f ( x ) = 9 - 7 x , g ( x ) = - 3 x + 7$ Find $( f + g ) ( x )$ .

Find the requested value. - $f ( x ) = - 3 x ^ { 2 } - 4 , g ( x ) = x - 1$ Find $f ( - 4 ) - g ( - 4 )$ .

Find the indicated function value. - $f ( x ) = 2 x - 5 , g ( x ) = 2 x ^ { 2 } + 2 x - 1$ Find $( f + g ) ( 4 )$ .

Find the indicated function value. - $f ( x ) = x ^ { 2 } + \frac { 1 } { 3 } x - 3 , g ( x ) = x ^ { 3 } - \frac { 2 } { 3 } x ^ { 2 } + x$ Find $( f + g ) ( x )$ .

Find the indicated function value. - $f ( x ) = 4 x ^ { 2 } - 4 , g ( x ) = 2 x ^ { 2 } - 2$ Find $( f + g ) ( 5 )$ .

Find the domain of the function. - $f ( x ) = x ^ { 2 } + 8$

Find the indicated function value. - $f ( x ) = x + 2 , g ( x ) = x + 7$ Find $( f + g ) ( 1 )$ .

Find the indicated function value. - $f ( x ) = 5 x ^ { 2 } + 7 x + 6 , g ( x ) = 3 x + 4$ Find $( f + g ) ( 5 )$ .

Quiz 2: Functions and Linear Functions

Find the indicated function value. - f(x) =4x+5,g(x) =−4x+3f ( x ) = 4 x + 5 , g ( x ) = - 4 x + 3f(x) =4x+5,g(x) =−4x+3 Find (f+g) (−1) ( f + g ) ( - 1 ) (f+g) (−1) .

For the pair of functions, determine the domain of f + g. - f(x) =5x−1,g(x) =4x−2f ( x ) = 5 x - 1 , g ( x ) = \frac { 4 } { x - 2 }f(x) =5x−1,g(x) =x−24​

Find the indicated function value. - f(x) =3x−1,g(x) =2x2−1f ( x ) = 3 x - 1 , g ( x ) = 2 x ^ { 2 } - 1f(x) =3x−1,g(x) =2x2−1 Find (f+g) (3) ( f + g ) ( 3 ) (f+g) (3) .

Find the domain of the function. - f(x) =1x−5+4x+10f ( x ) = \frac { 1 } { x - 5 } + \frac { 4 } { x + 10 }f(x) =x−51​+x+104​

Find the domain of the function. - f(x) =x−7x−3f ( x ) = x - \frac { 7 } { x - 3 }f(x) =x−x−37​

Find the domain of the function. - f(x) =xx2+8f ( x ) = \frac { x } { x ^ { 2 } + 8 }f(x) =x2+8x​

For the pair of functions, determine the domain of f + g. - f(x) =3x2+1,g(x) =5x3−7f ( x ) = 3 x ^ { 2 } + 1 , g ( x ) = 5 x ^ { 3 } - 7f(x) =3x2+1,g(x) =5x3−7

For the pair of functions, determine the domain of f + g. - f(x) =2xx−1,g(x) =4x+9f ( x ) = \frac { 2 x } { x - 1 } , g ( x ) = \frac { 4 } { x + 9 }f(x) =x−12x​,g(x) =x+94​

Find the requested value. - f(x) =−5x2−5x+8,g(x) =3x−8f ( x ) = - 5 x ^ { 2 } - 5 x + 8 , g ( x ) = 3 x - 8f(x) =−5x2−5x+8,g(x) =3x−8 Find f(−2) +g(−2) f ( - 2 ) + g ( - 2 ) f(−2) +g(−2) .

For the pair of functions, determine the domain of f + g. - f(x) =5x+5,g(x) =3x+1f ( x ) = 5 x + 5 , g ( x ) = \frac { 3 } { x + 1 }f(x) =5x+5,g(x) =x+13​

Find the domain of the function. - f(x) =−5xx+3f ( x ) = \frac { - 5 x } { x + 3 }f(x) =x+3−5x​

Find the indicated function value. - f(x) =2x2−2,g(x) =3x2+3x−3f ( x ) = 2 x ^ { 2 } - 2 , g ( x ) = 3 x ^ { 2 } + 3 x - 3f(x) =2x2−2,g(x) =3x2+3x−3 Find (f+g) (4) ( f + g ) ( 4 ) (f+g) (4) .

Find the indicated function value. - f(x) =9−7x,g(x) =−3x+7f ( x ) = 9 - 7 x , g ( x ) = - 3 x + 7f(x) =9−7x,g(x) =−3x+7 Find (f+g) (x) ( f + g ) ( x ) (f+g) (x) .

Find the requested value. - f(x) =−3x2−4,g(x) =x−1f ( x ) = - 3 x ^ { 2 } - 4 , g ( x ) = x - 1f(x) =−3x2−4,g(x) =x−1 Find f(−4) −g(−4) f ( - 4 ) - g ( - 4 ) f(−4) −g(−4) .

Find the indicated function value. - f(x) =2x−5,g(x) =2x2+2x−1f ( x ) = 2 x - 5 , g ( x ) = 2 x ^ { 2 } + 2 x - 1f(x) =2x−5,g(x) =2x2+2x−1 Find (f+g) (4) ( f + g ) ( 4 ) (f+g) (4) .

Find the indicated function value. - f(x) =x2+13x−3,g(x) =x3−23x2+xf ( x ) = x ^ { 2 } + \frac { 1 } { 3 } x - 3 , g ( x ) = x ^ { 3 } - \frac { 2 } { 3 } x ^ { 2 } + xf(x) =x2+31​x−3,g(x) =x3−32​x2+x Find (f+g) (x) ( f + g ) ( x ) (f+g) (x) .

Find the indicated function value. - f(x) =4x2−4,g(x) =2x2−2f ( x ) = 4 x ^ { 2 } - 4 , g ( x ) = 2 x ^ { 2 } - 2f(x) =4x2−4,g(x) =2x2−2 Find (f+g) (5) ( f + g ) ( 5 ) (f+g) (5) .

Find the domain of the function. - f(x) =x2+8f ( x ) = x ^ { 2 } + 8f(x) =x2+8

Find the indicated function value. - f(x) =x+2,g(x) =x+7f ( x ) = x + 2 , g ( x ) = x + 7f(x) =x+2,g(x) =x+7 Find (f+g) (1) ( f + g ) ( 1 ) (f+g) (1) .

Find the indicated function value. - f(x) =5x2+7x+6,g(x) =3x+4f ( x ) = 5 x ^ { 2 } + 7 x + 6 , g ( x ) = 3 x + 4f(x) =5x2+7x+6,g(x) =3x+4 Find (f+g) (5) ( f + g ) ( 5 ) (f+g) (5) .

Find the indicated function value. - $f ( x ) = 4 x + 5 , g ( x ) = - 4 x + 3$ Find $( f + g ) ( - 1 )$ .

For the pair of functions, determine the domain of f + g. - $f ( x ) = 5 x - 1 , g ( x ) = \frac { 4 } { x - 2 }$

Find the indicated function value. - $f ( x ) = 3 x - 1 , g ( x ) = 2 x ^ { 2 } - 1$ Find $( f + g ) ( 3 )$ .

Find the domain of the function. - $f ( x ) = \frac { 1 } { x - 5 } + \frac { 4 } { x + 10 }$

Find the domain of the function. - $f ( x ) = x - \frac { 7 } { x - 3 }$

Find the domain of the function. - $f ( x ) = \frac { x } { x ^ { 2 } + 8 }$

For the pair of functions, determine the domain of f + g. - $f ( x ) = 3 x ^ { 2 } + 1 , g ( x ) = 5 x ^ { 3 } - 7$

For the pair of functions, determine the domain of f + g. - $f ( x ) = \frac { 2 x } { x - 1 } , g ( x ) = \frac { 4 } { x + 9 }$

Find the requested value. - $f ( x ) = - 5 x ^ { 2 } - 5 x + 8 , g ( x ) = 3 x - 8$ Find $f ( - 2 ) + g ( - 2 )$ .

For the pair of functions, determine the domain of f + g. - $f ( x ) = 5 x + 5 , g ( x ) = \frac { 3 } { x + 1 }$

Find the domain of the function. - $f ( x ) = \frac { - 5 x } { x + 3 }$

Find the indicated function value. - $f ( x ) = 2 x ^ { 2 } - 2 , g ( x ) = 3 x ^ { 2 } + 3 x - 3$ Find $( f + g ) ( 4 )$ .

Find the indicated function value. - $f ( x ) = 9 - 7 x , g ( x ) = - 3 x + 7$ Find $( f + g ) ( x )$ .

Find the requested value. - $f ( x ) = - 3 x ^ { 2 } - 4 , g ( x ) = x - 1$ Find $f ( - 4 ) - g ( - 4 )$ .

Find the indicated function value. - $f ( x ) = 2 x - 5 , g ( x ) = 2 x ^ { 2 } + 2 x - 1$ Find $( f + g ) ( 4 )$ .

Find the indicated function value. - $f ( x ) = x ^ { 2 } + \frac { 1 } { 3 } x - 3 , g ( x ) = x ^ { 3 } - \frac { 2 } { 3 } x ^ { 2 } + x$ Find $( f + g ) ( x )$ .

Find the indicated function value. - $f ( x ) = 4 x ^ { 2 } - 4 , g ( x ) = 2 x ^ { 2 } - 2$ Find $( f + g ) ( 5 )$ .

Find the domain of the function. - $f ( x ) = x ^ { 2 } + 8$

Find the indicated function value. - $f ( x ) = x + 2 , g ( x ) = x + 7$ Find $( f + g ) ( 1 )$ .

Find the indicated function value. - $f ( x ) = 5 x ^ { 2 } + 7 x + 6 , g ( x ) = 3 x + 4$ Find $( f + g ) ( 5 )$ .