Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.1 Inverse Functions - 4.1 Exercises - Page 417: 44


$f$ and $g$ are not inverses of each other.

Work Step by Step

RECALL: (1) $(f \circ g)(x) = f\left(g(x)\right)$ (2) The function $g(x)$ is the inverse of function of a one-to-one function $(x)$ if for every element of the domain, $(f \circ g)(x) =x$ and $(g \circ f)(x)=x$ Find $(f \circ g)(x)$ by substituting $-\frac{1}{4}x-2$ to $x$ in $f(x)$: $(f\circ g)(x) \\=f\left(g(x)\right) \\=-4\left(-\frac{1}{4}x-2\right)+2 \\=-4(-\frac{1}{4}x)-2(-4)+2 \\=x+8+2 \\=x+10$ Since $(f\circ g)(x)\ne x$, then $f$ and $g$ are not inverses of each other.
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