Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 12 - Exponential Functions and Logarithmic Functions - 12.1 Composite Functions and Inverse Functions - 12.1 Exercise Set - Page 787: 18

Answer

$a.\quad(f\circ g)(1) = 4$ $b.\displaystyle \quad(g\circ f)(1) = \frac{13}{2}$ $c.\quad (f\circ g)(x) = \sqrt{\dfrac{13+3x}{x}} $ $d.\displaystyle \quad (g\circ f)(x) = \frac{13}{\sqrt{x+3}}$

Work Step by Step

$(f\circ g)(x)=f[g(x)]=\sqrt{g(x)+3}$ $= \sqrt{\frac{13}{x}+3}$ $= \sqrt{\dfrac{13+3x}{x}} \qquad ... \quad(c)$ $(f\circ g)(1)= \sqrt{\frac{13+3}{1}} =\sqrt{16}=4 \qquad ... \quad(a)$ $(g\displaystyle \circ f)(x)=g[f(x)]=\frac{13}{f(x)}$ $= \displaystyle \frac{13}{\sqrt{x+3}} \qquad ... \quad(d)$ $(g\displaystyle \circ f)(1)= \frac{13}{\sqrt{1+3}} =\frac{13}{2} \qquad ... \quad(b)$
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