Precalculus Examples

$f (x) = {\begin{cases} x^{2} - 2 & x \neq 0 \\ - 6 & x = 0 \end{cases}$ Find $f (- 1)$

Step 1

Identify the piece that describes the function at $x = - 1$ . In this case, $x = - 1$ falls within the interval $x \neq 0$ , therefore use $x^{2} - 2$ to evaluate $f (- 1)$ .

$f (x) = {\begin{cases} x^{2} - 2 & x \neq 0 \\ - 6 & x = 0 \end{cases}$

Step 2

The function is equal to $x^{2} - 2$ at $x = - 1$ .

$f (x) = x^{2} - 2 (]_{x = - 1}^{})$

Step 3

Evaluate the function at $x = - 1$ .

$f (- 1) = {(- 1)}^{2} - 2$

Step 4

Raise $- 1$ to the power of $2$ .

$f (- 1) = 1 - 2$

Step 5

Subtract $2$ from $1$ .

$f (- 1) = - 1$