Find g(f(x)) f(x)=1/(x-2) , g(x)=x^2

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

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (\frac{1}{x - 2})$ by substituting in the value of $f$ into $g$ .

$g (\frac{1}{x - 2}) = {(\frac{1}{x - 2})}^{2}$

Step 3

Apply the product rule to $\frac{1}{x - 2}$ .

$g (\frac{1}{x - 2}) = \frac{1^{2}}{{(x - 2)}^{2}}$

Step 4

One to any power is one.

$g (\frac{1}{x - 2}) = \frac{1}{{(x - 2)}^{2}}$