Question

In Exercises 17 to 26, use composition of functions to determine whether $f$ and $g$ are inverses of one another. $$ f(x)=3 x+2 ; g(x)=\frac{1}{3} x-\frac{2}{3} $$

Name: Problem 22, Chapter 4: College Algebra and Trigonometry
Uploaded: 2021-07-13T22:02:45-08:00
Duration: 58 s
Channel: James Kiss
Description: In Exercises 17 to 26, use composition of functions to determine whether f and g are inverses of one another. f(x)=3 x+2 ; g(x)=(1)/(3) x-(2)/(3)

   In Exercises 17 to 26, use composition of functions to determine whether $f$ and $g$ are inverses of one another.
$$
f(x)=3 x+2 ; g(x)=\frac{1}{3} x-\frac{2}{3}
$$

College Algebra and Trigonometry

Richard N. Aufmann,… 7th Edition

Chapter 4, Problem 22

Instant Answer

Solved by Expert James Kiss

07/13/2021

Step 1

1) $(f \circ g)(x) = f(g(x)) = f\left(\frac{1}{3}x - \frac{2}{3}\right)$ Now, we substitute the expression for $g(x)$ into the function $f(x)$: $f\left(\frac{1}{3}x - \frac{2}{3}\right) = 3\left(\frac{1}{3}x - \frac{2}{3}\right) + 2$ Simplify the Show more…

Show all steps

Thanks for your feedback!

In Exercises 17 to 26, use composition of functions to determine whether $f$ and $g$ are inverses of one another. $$ f(x)=3 x+2 ; g(x)=\frac{1}{3} x-\frac{2}{3} $$

Play audio

Feedback

James Kiss and 50 other educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Inverse Functions

An inverse function undoes the effect of the original function, meaning that if you apply the original function and then its inverse, you should return to your starting value. In other words, if f and g are inverses, then f(g(x)) = x and g(f(x)) = x for every x in the domains of g and f, respectively.

Composition of Functions

The composition of functions involves applying one function to the result of another function. This is denoted as (f ? g)(x) = f(g(x)). When checking for inverse functions, composing the functions in both orders should yield the original input, thereby confirming that the functions undo one another.

Identity Function

The identity function is the function that always returns the same value that was used as its input, written as I(x) = x. When two functions are inverses, their composition yields the identity function, which confirms that no alterations have been made to the original input.

Please give Ace some feedback