Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Section 2.8 - One-to-One Functions and Their Inverses - 2.8 Exercises - Page 226: 39

Answer

Since $f\circ g(x)=x$ and $g\circ f(x)=x$, f and g are inverses of each other.

Work Step by Step

$\begin{array}{lllll} f\circ g(x) & =f[g(x)] & ..... & g\circ f(x) & =g[f(x)]\\ & =3g(x)+4 & & & =\frac{f(x)-4}{3}\\ & =\frac{3(x-4)}{3}+4 & & & =\frac{3x+4-4}{3}\\ & =x-4+4 & & & =\frac{3x}{3}\\ & =x & & & =x \end{array}$ Since $f\circ g(x)=x$ and $g\circ f(x)=x$, f and g are inverses of each other.
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