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Help Algebra 2

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asked Apr 28, 2016 in ALGEBRA 2 by Doll_girl98 Novice

3 Answers

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(a)

Step 1:

The function is .

Rewrite the function as an equation relating and .

image

Exchange and in the equation.

image

Solve the equation for .

Replace with .

image

The inverse of is .

Solution:

The inverse function is .

answered Apr 28, 2016 by Anney Mentor
0 votes

(b)

Step 1:

The functions are and .

Find the Composition of functions.

Find .

Composition of functions formula: .

Substitute in the formula.

Substitute again in and simplify.

image

Find image.

Composition of functions formula: .

Substitute in the formula.

Substitute again in and simplify.

image

image

Therefore, image

Solution:

The functions image and image are inverses of each other.

answered Apr 28, 2016 by Anney Mentor
0 votes

(c)

Graph the functions.

From a:

Consider the functions are and .

Graph the functions and .

Observe the graph:

Since, the graph of image is the reflection of the graph of image in the line .

The functions image and image are inverses of each other.

answered Apr 28, 2016 by Anney Mentor

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