Algebra Examples

$f (x) = x^{- 2}$ $g (x) = \frac{(x - 1)}{3}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{x - 1}{3})$ by substituting in the value of $g$ into $f$ .

$f (\frac{x - 1}{3}) = {(\frac{x - 1}{3})}^{- 2}$

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

$f (\frac{x - 1}{3}) = {(\frac{3}{x - 1})}^{2}$

Step 4

Apply the product rule to $\frac{3}{x - 1}$ .

$f (\frac{x - 1}{3}) = \frac{3^{2}}{{(x - 1)}^{2}}$

Step 5

Raise $3$ to the power of $2$ .

$f (\frac{x - 1}{3}) = \frac{9}{{(x - 1)}^{2}}$