College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.2 - One-to-One Functions; Inverse Functions - 6.2 Assess Your Understanding - Page 420: 38

Answer

$f(g(x))=x$ and $g(f(x))=x$ therefore $f$ and $g$ are inverses of each other. Both $f(x)$ and $g(x)$ have the set of real numbers as a domain so the inverse has no domain restrictions.

Work Step by Step

Substitute $g(x)$ to $x$ in $ f(x)$ to obtain: \begin{align*} f\left(g(x)\right)&=2\left(\frac{1}{2}x-3\right)+6\\ &=x-6+6\\ &=x \end{align*} Substitute $f(x)$ to $x$ in $g(x)$ to obtain: \begin{align*} g\left(f(x)\right)&=\frac{1}{2}(2x+6)-3\\ &=x+3-3\\ &=x \end{align*} Since $f(g(x))=g(f(x))=x$, then $f$ and $g$ are inverses of each other. Both $f(x)$ and $g(x)$ have the set of real numbers as a domain so the inverse has no restrictions.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.