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 18: 9


$f\circ g\circ h\ =\ \sqrt{\frac{5x+1}{4x+1}}$

Work Step by Step

$f(x)=\sqrt{x+1}$ $g(x)=\frac{1}{x+4}$ $h(x)=\frac{1}{x}$ $f\circ g\circ h=f(g(h(x)))$ First evalulate the composition of the inner two function as: $g\circ h=g(h(x))$ $=\frac{1}{\frac{1}{x}+4}$ Smplify: $=\frac{x}{1+4x}$ Now find the remaining part as: $f\circ g\circ h=f(g(h(x)))$ $f(\frac{x}{1+4x})=\sqrt{\frac{x}{1+4x}+1}$ Simplify: $=\sqrt{\frac{5x+1}{4x+1}}$
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