Question 1

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

Accepted Answer

The answer of Graph the given function. f(x) = (x...

Question 2

Use the functions given by and g(x) = x³ to find (g^-1 _º f^-1)(-5).

Accepted Answer

The answer of Use the functions given by  and...

Question 3

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|

Accepted Answer

To ensure the function $f(x) = |x + 5|$ is one-to-one, we restrict its domain to $x \geq -5$, where it is monotonically increasing. The inverse function is $f^{-1}(x) = x - 5$, as it undoes the effect of $f$ under this restriction. The domain of $f$ and the range of $f^{-1}$ are $x \geq -5$, and the domain of $f^{-1}$ and the range of $f$ are $x \geq 0$, matching the conditions in choice A.

Question 4

Use the functions given by and g(x) = x³ to find the indicated value. (f _º g)^-1(5)

Accepted Answer

The answer of ​Use the functions given by  and...

Question 5

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

Accepted Answer

The answer of Use the functions given by f(x) =...

Question 6

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

Accepted Answer

The given function is not one-to-one, which means that multiple inputs can result in the same output. Therefore, there cannot be a unique inverse function for every possible output. Thus, there is no inverse function for the given function.

Question 7

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.

Accepted Answer

To find the inverse function, we need to isolate x. y = 0.03x² + 245.50 y - 245.50 = 0.03x² Divide both sides by 0.03². (y - 245.50) / 0.03² = x Therefore, the inverse function is: x = (y - 245.50) / 0.03² Which is equivalent to: f^(-1)(y) = (y - 245.50) / 0.03² So, the correct answer is B.

Question 8

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

Accepted Answer

The answer of Restrict the domain of f(x) = x²...

Question 9

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

Accepted Answer

The answer of Restrict the domain of the function f...

Question 10

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

Accepted Answer

To ensure the function $f(x) = |x - 9| + 1$ is one-to-one, we restrict the domain to $x \geq 9$. For $x \geq 9$, $f(x) = (x - 9) + 1 = x - 8$. The inverse function $f^{-1}(x)$ would then swap $x$ and $y$, leading to $x = y - 8$ or $y = x + 8$, which matches choice A. The domain of $f$ and the range of $f^{-1}$ are $x \geq 9$, and the domain of $f^{-1}$ and the range of $f$ are $x \geq 1$, as $f(x)$ starts from 1 when $x = 9$.

Question 11

Use the functions given by and g(x) = x³ to find (f^-1 _º f^-1)(-5).

Accepted Answer

The answer of Use the functions given by  and...

Question 12

Use the functions given by and g(x) = x³ to find (f^-1 _º g^-1)(1).

Accepted Answer

The answer of Use the functions given by  and...

Question 13

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

Accepted Answer

The answer of Determine whether the function has an inverse...

Question 14

Use the functions given by and g(x) = x³ to find g^-1 _º f^-1.

Accepted Answer

The answer of Use the functions given by  and...

Question 15

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

Accepted Answer

The given function is an encryption function that maps a message to a coded message. The encryption function is one-to-one and onto. Therefore, it has an inverse function, which is the decryption function. Choice C represents the decryption function that maps a coded message to its original message.

Question 16

Use the functions given by and g(x) = x³ to find (f _º g)^-1.

Accepted Answer

First, we need to evaluate f S1U1B1ºS1U1B0 g.

Using the definition of composition of functions:

(f S1U1B1ºS1U1B0 g)(x) = f(S1U1B1(S1U1B0 x)) = f(S1U1P1(x + 2)) = (x + 2)S1U1P13S1S1P0

Next, we need to apply S1U1P1-1S1S1P0 to the result:

((f S1U1B1ºS1U1B0 g)S1U1P1-1S1S1P0)(x) = (f S1U1B1ºS1U1B0 g)(S1U1P1-1S1S1P0 x)

We have:

S1U1P1-1S1S1P0 x = (x - 1)S1S1P0 = xS1S1U1P1S1S1P0S1S1P0

Therefore:

((f S1U1B1ºS1U1B0 g)S1U1P1-1S1S1P0)(x) = (f S1U1B1ºS1U1B0 g)(xS1S1U1P1S1S1P0S1S1P0)

= ((x + 2)S1U1P13S1S1P0)S1S1U1P1S1S1P0S1S1P0

= (x + 2)S1U1P13S1U1P1S1S1P0

= 11eacce6_2229_2ed5_9f49_f95b88e62577_TB7896_11

Therefore, the answer is C.

Question 17

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? ​

Accepted Answer

The answer of Your wage is $11.00 per hour plus...

Question 18

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

Accepted Answer

First, we need to find g(f(2)). Starting with f(2): f(2) = 2 + 6 = 8 Now, plugging in f(2) into g(x): g(f(2)) = g(8) = 7(8) - 3 = 53 Next, we need to find f(g(1)). Starting with g(1): g(1) = 7(1) - 3 = 4 Now, plugging in g(1) into f(x): f(g(1)) = f(4) = 4 + 6 = 10 Finally, we need to find f(g(-1)), which follows the same process as above: g(-1) = 7(-1) - 3 = -10 f(g(-1)) = f(-10) = -10 + 6 = -4 Putting it all together: g^-1 _º f^-1 = 53 _º10 -4 The only answer choice that matches this is C.

Question 19

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

Accepted Answer

The answer of Restrict the domain of the function f...

Question 20

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

Accepted Answer

The given function is not one-to-one, as different input values can yield the same output value. For example, f(0) = f(5) = 5. Therefore, it does not have an inverse function.

Quiz 7: Prerequisites

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

Use the functions given by and g(x) = x³ to find (g^-1 _º f^-1) (-5) .

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|

Use the functions given by and g(x) = x³ to find the indicated value. (f _º g) ^-1(5)

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

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

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.

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

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

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

Use the functions given by and g(x) = x³ to find (f^-1 _º f^-1) (-5) .

Use the functions given by and g(x) = x³ to find (f^-1 _º g^-1) (1) .

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

Use the functions given by and g(x) = x³ to find g^-1 _º f^-1.

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

Use the functions given by and g(x) = x³ to find (f _º g) ^-1.

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?

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

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

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

Quiz 7: Prerequisites

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

Use the functions given by and g(x) = x3 to find (g-1 º f-1) (-5) . ​

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| ​

​Use the functions given by and g(x) = x3 to find the indicated value. (f º g) -1(5)

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

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

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. ​

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

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 ​

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 ​

Use the functions given by and g(x) = x3 to find (f-1 º f-1) (-5) . ​

Use the functions given by and g(x) = x3 to find (f-1 º g-1) (1) . ​

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

Use the functions given by and g(x) = x3 to find g-1 º f-1. ​

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

Use the functions given by and g(x) = x3 to find (f º g) -1. ​

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? ​

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

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 ​

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

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

Use the functions given by and g(x) = x³ to find (g^-1 _º f^-1) (-5) .

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|

Use the functions given by and g(x) = x³ to find the indicated value. (f _º g) ^-1(5)

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

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

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.

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

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

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

Use the functions given by and g(x) = x³ to find (f^-1 _º f^-1) (-5) .

Use the functions given by and g(x) = x³ to find (f^-1 _º g^-1) (1) .

Use the functions given by and g(x) = x³ to find g^-1 _º f^-1.

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

Use the functions given by and g(x) = x³ to find (f _º g) ^-1.

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?

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

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

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