Find f(g(x)) f(x)=4/x , g(x)=4/(x^2)

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{4}{x^{2}})$ by substituting in the value of $g$ into $f$ .

$f (\frac{4}{x^{2}}) = \frac{4}{\frac{4}{x^{2}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$f (\frac{4}{x^{2}}) = 4 (\frac{x^{2}}{4})$

Step 4

Cancel the common factor of $4$ .

Cancel the common factor.

$f (\frac{4}{x^{2}}) = 4 (\frac{x^{2}}{4})$

Rewrite the expression.

$f (\frac{4}{x^{2}}) = x^{2}$