Precalculus Examples

$f (x) = {\begin{cases} - {(x + 2)}^{2} + 8 & x \neq - 5 \\ 0 & x = - 5 \end{cases}$ Find $f (1)$

Step 1

Identify the piece that describes the function at $x = 1$ . In this case, $x = 1$ falls within the interval $x \neq - 5$ , therefore use $- {(x + 2)}^{2} + 8$ to evaluate $f (1)$ .

$f (x) = {\begin{cases} - {(x + 2)}^{2} + 8 & x \neq - 5 \\ 0 & x = - 5 \end{cases}$

Step 2

The function is equal to $- {(x + 2)}^{2} + 8$ at $x = 1$ .

$f (x) = - {(x + 2)}^{2} + 8 (]_{x = 1}^{})$

Step 3

Evaluate the function at $x = 1$ .

$f (1) = - {((1) + 2)}^{2} + 8$

Step 4

Simplify each term.

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Step 4.1

Add $1$ and $2$ .

$f (1) = - 3^{2} + 8$

Step 4.2

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

$f (1) = - 1 \cdot 9 + 8$

Step 4.3

Multiply $- 1$ by $9$ .

$f (1) = - 9 + 8$

Step 5

Add $- 9$ and $8$ .

$f (1) = - 1$