Answer
$ g(x)=\frac{2x}{x-1}$
Work Step by Step
Since $ f(g)=x $, we have $\frac{g}{g-2}=x $
Solve the equation:
$g=x(g-2)$
$g=gx-2x$
$2x=gx-g$
$2x=g(x-1)$
$ g=\frac{2x}{x-1}$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 1: Functions - Section 1.2 - Combining Functions; Shifting and Scaling Graphs - Exercises 1.2 - Page 19: 19
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