Precalculus Examples

$f (x) = {\begin{cases} {(x + 7)}^{2} - 7 & x \neq - 4 \\ 3 & x = - 4 \end{cases}$ Find $f (- 5)$

Step 1

Identify the piece that describes the function at $x = - 5$ . In this case, $x = - 5$ falls within the interval $x \neq - 4$ , therefore use ${(x + 7)}^{2} - 7$ to evaluate $f (- 5)$ .

$f (x) = {\begin{cases} {(x + 7)}^{2} - 7 & x \neq - 4 \\ 3 & x = - 4 \end{cases}$

Step 2

The function is equal to ${(x + 7)}^{2} - 7$ at $x = - 5$ .

$f (x) = {(x + 7)}^{2} - 7 (]_{x = - 5}^{})$

Step 3

Evaluate the function at $x = - 5$ .

$f (- 5) = {((- 5) + 7)}^{2} - 7$

Step 4

Simplify each term.

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Step 4.1

Add $- 5$ and $7$ .

$f (- 5) = 2^{2} - 7$

Step 4.2

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

$f (- 5) = 4 - 7$

Step 5

Subtract $7$ from $4$ .

$f (- 5) = - 3$