Express the given function as a composite of functions f and g such that y $$y = f ( g ( x ) )$$
-$$y = \frac { 1 } { x ^ { 2 } - 5 }$$
A) $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = - \frac { 1 } { 5 }$
B) $f ( x ) = \frac { 1 } { x ^ { 2 } } , g ( x ) = x - 5$
C) $f ( x ) = \frac { 1 } { x } , g ( x ) = x ^ { 2 } - 5$
D) $f ( x ) = \frac { 1 } { 5 } , g ( x ) = x ^ { 2 } - 5$

Question

Quizplus · Accepted Answer

We can rewrite the given function as $y=\frac{1}{x^2}-\frac{1}{5}$, which suggests the choice of $f(x)=\frac{1}{x}$ and $g(x)=x^2-5$. This is because $g(x)$ produces the term $x^2-5$ which, when plugged into $f(x)$, gives $\frac{1}{x^2-5}$, matching the given function. Therefore, the answer is C.

Express the Given Function as a Composite of Functions F y=f(g(x))y = f ( g ( x ) )y=f(g(x))

Express the Given Function as a Composite of Functions F $y = f ( g ( x ) )$