Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Section 2.7 - Combining Functions - 2.7 Exercises - Page 217: 50

Answer

$f\circ g(x)=x+2;\qquad $ domain: all reals, $(-\infty,\infty)$ $ g\circ f(x)=\sqrt[3]{x^{3}+2}; \quad$ domain: all reals, $(-\infty,\infty)$ $ f\circ f(x)=(x^{3}+2)^{3}+2 ;\quad$ domain: all reals, $(-\infty,\infty)$ $ g\circ g(x)=\sqrt[9]{x}; \quad$ domain: all reals, $(-\infty,\infty)$

Work Step by Step

f(x) is defined for all x, g(x) is defined for all x $f\circ g(x)=f[g(x)]=[g(x)]^{3}+2$ $=(\sqrt[3]{x})^{3}+2$ $=x+2;\qquad $ domain: all reals, $(-\infty,\infty)$ $g\circ f(x)=g[f(x)]=\sqrt[3]{f(x)}$ $=\sqrt[3]{x^{3}+2}; \quad$ domain: all reals, $(-\infty,\infty)$ $f\circ f(x)=f[f(x)]=[f(x)]^{3}+2$ $=(x^{3}+2)^{3}+2 ;\quad$ domain: all reals, $(-\infty,\infty)$ $g\circ g(x)=g[g(x)]=\sqrt[3]{g(x)}$ $=\sqrt[3]{=\sqrt[3]{x}}$ $=\sqrt[9]{x}; \quad$ domain: all reals, $(-\infty,\infty)$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.