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: 41

Answer

f(g(x))= x g(f(x))= x

Work Step by Step

The question asks to prove that f and g are inverses of each other. So, to be able to solve for f(x), first, you replace the (x) by g(x). G(x) is $\frac{1}{x}$, so you replace g(x) by $\frac{1}{x}$. Then you solve for f(x). Meaning that the x in the f(x) equation is going to be replaced by $\frac{1}{x}$. Then you solve. 1 over $\frac{1}{x}$ equals to $\frac{1}{1}$$\times$$\frac{x}{1}$. It equals to $\frac{x}{1}$, which can be simplified to x. Same process for g(x). These equations say that the cube function and the cube root function, when composed, cancel each other.
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