Thomas' Calculus 13th Edition

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: 18

Answer

$ f(g(x))=(1-\sqrt x)^{2}$, Domain: $[0,\infty)$, Range: $(0,\infty)$ $ g(f(x))=1-|x|$, Domain: $(-\infty,\infty)$, Range: $(-\infty,1]$

Work Step by Step

To find the composite function, we plug in the inside function into the "x" value of the outside function: $f\circ g = f(g(x))=(1-\sqrt x)^{2}$ $g\circ f = g(f(x))=1-\sqrt {x^{2}}=1-|x|$
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