Precalculus Examples

$f (x) = {\begin{cases} - {(x + 1)}^{2} - 4 & x < 1 \\ x - 7 & 1 \leq x \leq 6 \\ 4 & x > 6 \end{cases}$ Find $f (7)$

Step 1

Identify the piece that describes the function at $x = 7$ . In this case, $x = 7$ falls within the interval $x > 6$ , therefore use $4$ to evaluate $f (7)$ .

$f (x) = {\begin{cases} - {(x + 1)}^{2} - 4 & x < 1 \\ x - 7 & 1 \leq x \leq 6 \\ 4 & x > 6 \end{cases}$

Step 2

The function is equal to $4$ at $x = 7$ .

$f (x) = 4 (]_{x = 7}^{})$

Step 3

Evaluate the function at $x = 7$ .

$f (7) = 4$