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 18: 8


$(f\circ g\circ h)(x)=6x^2+1.$

Work Step by Step

We are given $f(x)=3x+4$, $g(x)=2x-1$, and $h(x)=x^2$. So: $$(f\circ g\circ h)(x)=f(g(h(x)))=f(g(x^2))=f(2x^2-1)=3(2x^2-1)+4\\=6x^2-3+4 =6x^2+1.$$
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