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Expert-verified Found in: Page 348 ### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465 # Evaluate each expression using the graphs of y = f(x) and y = g(x) shown in the figure. (a) (g o f)(-8)(b) (fog)(-8)(c) (g o g)(7)(d) (g o f)(-5)

(a) -4

(b) 1

(c) -6

(d) -6

See the step by step solution

## Step 1: Given Information

Graph of two functions are given ## Part(a) : Step (1) : composition of functions

$\left(gof\right)\left(-8\right)\phantom{\rule{0ex}{0ex}}g\left(f\left(-8\right)\right)\phantom{\rule{0ex}{0ex}}fromthegraphf\left(-8\right)\phantom{\rule{0ex}{0ex}}f\left(-8\right)=2\phantom{\rule{0ex}{0ex}}g\left(f\left(-8\right)\right)=f\left(2\right)=-4\phantom{\rule{0ex}{0ex}}g\left(f\left(-8\right)\right)=-4$

## Part (b): Step 1: composition of function

$\left(fog\right)\left(-8\right)\phantom{\rule{0ex}{0ex}}f\left(g\left(-8\right)\right)\phantom{\rule{0ex}{0ex}}fromthegraphg\left(-8\right)=-2\phantom{\rule{0ex}{0ex}}f\left(g\left(-8\right)\right)=f\left(-2\right)=1\phantom{\rule{0ex}{0ex}}\left(fog\right)\left(-8\right)=1\phantom{\rule{0ex}{0ex}}$

## Part(c) : Step 1 : composition of functions

$\left(gog\right)\left(7\right)\phantom{\rule{0ex}{0ex}}g\left(g\left(7\right)\right)=g\left(0\right)=-6\phantom{\rule{0ex}{0ex}}\left(gog\right)\left(7\right)=-6$

## Part(d): Step 1: composition of functions

$\left(gof\right)\left(-5\right)\phantom{\rule{0ex}{0ex}}g\left(f\left(-5\right)\right)\phantom{\rule{0ex}{0ex}}thevalueoff\left(-5\right)is4\phantom{\rule{0ex}{0ex}}g\left(f\left(-5\right)\right)=g\left(4\right)=-6\phantom{\rule{0ex}{0ex}}\left(gof\right)\left(-5\right)=-6$ ### Want to see more solutions like these? 