Specify the domain of $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \frac { 5 } { x } \text { and } g ( x ) = 7 x - 5$
A) $( - \infty , 0 ) \cup ( 0 , \infty )$
B) $( 0 , \infty )$
C) $( - \infty , 0 )$
D) $( - \infty , \infty )$

Question

Quizplus · Accepted Answer

The domain of $g \circ f$ is determined by the domain of $f(x) = \frac{5}{x}$, which excludes $x = 0$ to avoid division by zero. Thus, the domain is all real numbers except 0, represented as $(- \infty , 0 ) \cup ( 0 , \infty )$.

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Specify the Domain Of $( g \circ f ) ( x )$