Find f(x)and g(x)such that h(x)= (f ° g)(x).
-$$h ( x ) = \frac { 1 } { x ^ { 2 } - 5 }$$
A) $f ( x ) = \frac { 1 } { 5 } , g ( x ) = x ^ { 2 } - 5$
B) $f ( x ) = \frac { 1 } { x } , g ( x ) = x ^ { 2 } - 5$
C) $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = x - 5$
D) $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = - \frac { 1 } { 5 }$

Question

Quizplus · Accepted Answer

If we let $g(x) = x^2 - 5$, then $f(g(x)) = \frac{1}{x^2-5}$. Taking $f(x) = \frac{1}{x}$ satisfies this, so $f(x) = \frac{1}{x}$ and $g(x) = x^2-5$ is a valid choice.

Find F(x)and G(x)such That H(x)= (F ° G)(x) h(x)=1x2−5h ( x ) = \frac { 1 } { x ^ { 2 } - 5 }h(x)=x2−51​

Find F(x)and G(x)such That H(x)= (F ° G)(x) $h ( x ) = \frac { 1 } { x ^ { 2 } - 5 }$