Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.7 - Combinations of Functions; Composite Functions - Concept and Vocabulary Check - Page 257: 16


If $f\left( g\left( x \right) \right)=-\frac{3}{g\left( x \right)-4}$ and $g\left( x \right)=\frac{8}{x}$ then 0 and $2$ must be excluded from the domain of $f\circ g$.

Work Step by Step

Consider the given expressions: $f\left( g\left( x \right) \right)=-\frac{3}{g\left( x \right)-4}$ And $g\left( x \right)=\frac{8}{x}$ Substitute $g\left( x \right)$ in the above expression, $f\left( g\left( x \right) \right)=-\frac{3}{\frac{8}{x}-4}$ Hence, the real numbers that are to be excluded from the expression will be $0$ and $2$.
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