Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 4 - Exponential and Logarithmic Functions - Section 4.1 Composite Functions - 4.1 Assess Your Understanding - Page 280: 65


a) $acx+ad+b $ b) $acx+cb+d$ c) domain for both (a) and (b): all real numbers d) $ad+b=cb+d$

Work Step by Step

We have the composite functions: a) $(f\circ g) (x) =f[g(x)]=a(cx+d)+b\\=acx+ad+b $ b) $(g\circ f) (x) = g[f(x)]=c(ax+b) +d=acx+cb+d$ c) The domain of both composite functions is all real numbers (no restrictions). d) The functions $f(x)$ and $g(x)$ are known as inverse functions. So, we can equate $(f\circ g) (x)=(g\circ f) (x)$ or, $f[g(x)]=g[f(x)]$ as follows: $acx+ad+b=acx+cb+d \\ ad+b=cb+d$
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