University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 1 - Section 1.2 - Combining Functions; Shifting and Scaling Graphs - Exercises - Page 19: 12


$a.\quad f\circ j$ $b.\quad g\circ h$ $c.\quad h\circ h$ $d.\quad f\circ f$ $e.\quad j\circ g\circ f$ $f.\quad g\circ f\circ h$

Work Step by Step

$f(x)=x-3$ $g(x)=\sqrt{x}$ $h(x)=x^3$ $j(x)=2x$ $a.\quad 2x-3=(2x)-3=f(2x)=f(j(x))$ $b.\quad x^{\frac{3}{2}}=\sqrt{x^3}=g(x^3)=g(h(x))$ $c.\quad x^9=(x^3)^3=h(x^3)=h(h(x))$ $d.\quad x-6=(x-3)-3=f(x-3)=f(f(x))$ $e.\quad 2\sqrt{x-3}=2(\sqrt{(x-3)})=j(g(f(x)))$ $f.\quad \sqrt{x^3-3}=\sqrt{(x^3)-3}=g(f(h(x)))$
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