Answered: EXAMPLE 8 More composite functions…

EXAMPLE 8 More composite functions Given f1x2 = Vx and g1x2 = x² - x - 6, find the following composite functions and their domains. %3D a. g'f b. g•g

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.7: Operations On Functions

Problem 55E

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Question

EXAMPLE 8 More composite functions Given f1x2 = Vx and g1x2 = x² - x - 6,
find the following composite functions and their domains.
%3D
a. g'f
b. g•g

Expert Solution

Step 1

Given: $f (x) = \sqrt[3]{x}, g (x) = x^{2} - x - 6$

we know that

domain of given function $f (x)$ is $x \geq 0$ and $g (x)$ is $x \in R .$

so, for finding $(g o f) (x)$ , we put $x = f (x)$ in $g (x)$

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