Precalculus Examples

$f (x) = {\begin{cases} {(x - 3)}^{2} - 2 & x \neq 3 \\ 2 & x = 3 \end{cases}$ Find $f (3)$

Step 1

Identify the piece that describes the function at $x = 3$ . In this case, $x = 3$ falls within the interval $x = 3$ , therefore use $2$ to evaluate $f (3)$ .

$f (x) = {\begin{cases} {(x - 3)}^{2} - 2 & x \neq 3 \\ 2 & x = 3 \end{cases}$

Step 2

The function is equal to $2$ at $x = 3$ .

$f (x) = 2 (]_{x = 3}^{})$

Step 3

Evaluate the function at $x = 3$ .

$f (3) = 2$