Determine $( g \circ f ) ( x )$ for the pair of functions $f ( x ) = \frac { 3 } { x } \text { and } g ( x ) = | x |$
A) $- \frac { 3 } { | x | }$
B) $\frac { 3 } { x }$
C) $\frac { 3 } { | x | }$
D) $\frac { | x | } { 3 }$

Question

Quizplus · Accepted Answer

$( g \circ f ) ( x )$ means we take the output of f and input it into g. Therefore,
$$( g \circ f ) ( x ) = g(f(x)) = g\left(\frac{3}{x}\right) = \left|\frac{3}{x}\right| = \frac{3}{|x|}$$
So the correct answer is C.

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