Find f(x) and g(x) so that the function can be described as y = f(g(x)).
-$$y = \frac { 1 } { x ^ { 2 } - 4 }$$
A) $f ( x ) = \frac { 1 } { 4 } , g ( x ) = x ^ { 2 } - 4$
B) $f ( x ) = \frac { 1 } { x } , g ( x ) = x ^ { 2 } - 4$
C) $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = x - 4$
D) $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = - 1 / 4$

Question

Quizplus · Accepted Answer

The correct choice is B because $f(g(x))$ requires that $g(x)$ be substituted into $f(x)$. Here, $g(x) = x^2 - 4$ is the inner function that modifies $x$ first, and then $f(x) = \frac{1}{x}$ takes the result of $g(x)$ and finds its reciprocal, matching the original function $y = \frac{1}{x^2 - 4}$.

Find F(x) and G(x) So That the Function Can Be y=1x2−4y = \frac { 1 } { x ^ { 2 } - 4 }y=x2−41​

Find F(x) and G(x) So That the Function Can Be $y = \frac { 1 } { x ^ { 2 } - 4 }$