Answer
$\{x|x\ne-4,0\}$.
Work Step by Step
Step 1. Domain of $g(x)$: $\{x|x\ne0 \}$.
Step 2. For $(f\circ g)(x)$: $g(x)-1\ne0 \Longrightarrow -\frac{4}{x}-1\ne0 \Longrightarrow x\ne-4$.
Step 3. Thus Domain of $(f\circ g)(x)$: $\{x|x\ne-4,0\}$.
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 4 - Exponential and Logarithmic Functions - Section 4.1 Composite Functions - 4.1 Assess Your Understanding - Page 280: 23
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