College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 4 - Section 4.1 - Inverse Functions - 4.1 Exercises - Page 395: 47

Answer

No.

Work Step by Step

The two functions are inverses if: $(f\circ g)(x)=x$ and $(g\circ f)(x) = x$; $x\ne (-6) x\ne 0$ Here, $f(g(x))=\frac{2}{\frac{6x+2}{x}+6}$. After multiplying $x$ to both the numerator and the denominator, we get: $\frac{2x}{6x+2+6x}=\frac{2x}{12x+2}\ne x$ Therefore, $f$ and $g$ are not inverses.
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