Find $( f g ) ( x )$ . $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = \frac { 1 } { x ^ { 4 } }$
A) $\frac { 1 } { x ^ { 4 } }$
B) $\frac { 1 } { x ^ { 2 } }$
C) $\frac { 1 } { x ^ { 6 } }$
D) $x ^ { 6 }$
E) $\frac { x ^ { 4 } } { x ^ { 2 } }$

Question

Find $( f g ) ( x )$ .   $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = \frac { 1 } { x ^ { 4 } }$ 
A) $\frac { 1 } { x ^ { 4 } }$
B) $\frac { 1 } { x ^ { 2 } }$
C) $\frac { 1 } { x ^ { 6 } }$
D) $x ^ { 6 }$
E) $\frac { x ^ { 4 } } { x ^ { 2 } }$

Quizplus · Accepted Answer

The composition $( f g ) ( x )$ means applying $g(x)$ first and then $f$, resulting in $f(g(x)) = f\left(\frac{1}{x^4}\right) = \frac{1}{\left(\frac{1}{x^4}\right)^2} = \frac{1}{x^8}$. However, the correct interpretation of the question seems to be finding the product $f(x)g(x)$, which is $\frac{1}{x^2} \cdot \frac{1}{x^4} = \frac{1}{x^6}$.

Find (fg)(x)( f g ) ( x )(fg)(x) f(x)=1x2,g(x)=1x4f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = \frac { 1 } { x ^ { 4 } }f(x)=x21​,g(x)=x41​

Find $( f g ) ( x )$ $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = \frac { 1 } { x ^ { 4 } }$