Functions

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Pre-Calculus › Functions

Questions 1 - 10

1

Find the inverse of .

$y = \frac{x+1}{10}$

$y = \frac{x-1}{10}$

$x = \frac{y - 1}{10}$

Explanation

To find the inverse of the function, we switch the switch the and variables in the function.

Switching and gives

Then, solving for gives our answer:

$\frac{x-1}{10} = y$

2

Determine the value of of the function

$f(x)=\sqrt{71-x}$

$f(7)=\sqrt{78}$

$f(7),, \textsc{dne}$

Explanation

In order to determine the value of of the function we set The value becomes

$f(7)=\sqrt{71-7}=\sqrt{64}=8$

As such

3

Find the inverse of .

$y = \frac{x+1}{10}$

$y = \frac{x-1}{10}$

$x = \frac{y - 1}{10}$

Explanation

To find the inverse of the function, we switch the switch the and variables in the function.

Switching and gives

Then, solving for gives our answer:

$\frac{x-1}{10} = y$

4

Find the inverse of .

$y = \frac{x+1}{10}$

$y = \frac{x-1}{10}$

$x = \frac{y - 1}{10}$

Explanation

To find the inverse of the function, we switch the switch the and variables in the function.

Switching and gives

Then, solving for gives our answer:

$\frac{x-1}{10} = y$

5

Determine the value of of the function

$f(x)=\sqrt{71-x}$

$f(7)=\sqrt{78}$

$f(7),, \textsc{dne}$

Explanation

In order to determine the value of of the function we set The value becomes

$f(7)=\sqrt{71-7}=\sqrt{64}=8$

As such

6

Determine the value of of the function

$f(x)=\sqrt{71-x}$

$f(7)=\sqrt{78}$

$f(7),, \textsc{dne}$

Explanation

In order to determine the value of of the function we set The value becomes

$f(7)=\sqrt{71-7}=\sqrt{64}=8$

As such

7

Find given

and

Explanation

To evaluate, first evaluate and then plug in that answer into . Thus,

Then, is

8

Find the inverse of the follow function:

$y=\pm\sqrt{\frac{x+9}{3}}$

$y=\sqrt{\frac{x-9}{3}}$

$y=\frac{1}{3x^2+9}$

$y=\frac{1}{3x^2-9}$

Explanation

To find the inverse, substitute all x's for y's and all y's for x's and then solve for y.

$\frac{x+9}{3}=y^2$

$y=\pm\sqrt{\frac{x+9}{3}}$

9

Find given

and

Explanation

To evaluate, first evaluate and then plug in that answer into . Thus,

Then, is

10

Find if and .

Explanation

Replace and substitute the value of into so that we are finding .

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