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: 60

Answer

$f\circ g\circ h=\dfrac{1}{(x^{2}+2)^{3}}$

Work Step by Step

$f(x)=\dfrac{1}{x}$ $,$ $g(x)=x^{3}$ $,$ $h(x)=x^{2}+2$ First, find $g\circ h$ by substituting $x$ by $h(x)$ in $g(x)$ and simplifying if possible: $g\circ h=g(h(x))=(x^{2}+2)^{3}$ Finally, to find $f\circ g\circ h$, substitute $x$ by $(x^{2}+2)^{3}$ in $f(x)$ and again, simplify if possible: $f\circ g\circ h=f(g(h(x)))=\dfrac{1}{(x^{2}+2)^{3}}$
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.