Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \frac { 1 } { x } \text { and } g ( x ) = \frac { 1 } { x - 7 }$
A) $\frac { 1 } { x - 7 x ^ { 2 } }$
B) $\frac { x } { 1 - 7 x }$
C) $\frac { 7 x } { 1 - 7 x }$
D) $\frac { x } { 7 - x }$

Question

Quizplus · Accepted Answer

To find $(g \circ f)(x)$, we substitute $f(x)$ into $g(x)$. So, $g(f(x)) = g\left(\frac{1}{x}\right) = \frac{1}{\frac{1}{x} - 7} = \frac{x}{1 - 7x}$, which matches choice B.

Determine (g∘f)(x)( g \circ f ) ( x )(g∘f)(x) For the Pair of Functions

Determine $( g \circ f ) ( x )$ For the Pair of Functions