Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 1: Functions - Practice Exercises - Page 37: 38


$ f(g(x))=\sqrt[4] {1-x}$, Domain $(-\infty,1]$, Range $[0,\infty)$ $ g(f(x))=\sqrt {1-\sqrt x}$, Domain $[0,1]$, Range $[0,1]$

Work Step by Step

The composite functions are computed by taking the inside function and placing it into the "x" value of the outside function: $f\circ g=f(g(x))$ The domain of any function consists of the values it can take on the x-axis, whereas the range consists of the value it can take on the y-axis. These values can be confirmed by graphing the function.
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