Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 2 - 2.7 - Inverse Functions - 2.7 Exercises - Page 228: 27

Answer

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Work Step by Step

We are given the functions: $f(x)=\sqrt{x+5}$ $g(x)=x^2-5, x\geq 0$ a) Verify that the two functions are inverse functions. Determine $f\circ g$ and $g\circ f$: $(f\circ g)(x)=f(g(x))=f\left(x^2-5\right)=\sqrt {x^2-5+5}=\sqrt{x^2}=|x|=x$ $(g\circ f)(x)=g(f(x))=g\left(\sqrt{x+5}\right)=(\sqrt{x+5})^2-5=x+5-5=x$ We got: $(f\circ g)(x)=(g\circ f)(x)=x$, therefore the two functions are inverse functions. b) Graph $f$ and $g$ and the line $y=x$. The graphs of $f$ and $g$ are symmetric with respect to the line $y=x$; therefore $f$ and $g$ are inverse functions.
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