Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.1 Composite Functions - 5.1 Assess Your Understanding - Page 255: 54



Work Step by Step

$(f\circ f)(x)=f(f(x))=f(\frac{x}{x-1})=\dfrac{\frac{x}{x-1}}{\frac{x}{x-1}-1}=\dfrac{\frac{x}{x-1}}{\frac{x}{x-1}-\frac{x-1}{x-1}}=\dfrac{\frac{x}{x-1}}{\frac{1}{x-1}}=\frac{x}{1}=x.$
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