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

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

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

Step 3

Simplify the numerator.

Rewrite $1$ as $1^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 1$ .

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