Question

f(x) = \

$$\begin{cases} -(x + 8)^2 + 1 & \\text{for } x \\leq -5 \\\\ 2x + 8 & \\text{for } x \\geq -2 \\end{cases}$$

find f(-7)

Explanation:

Step1: Determine the applicable function

Check the domain for \( x = -7 \). Since \( -7 \leq -5 \), we use \( f(x) = -(x + 8)^2 + 1 \).

Step2: Substitute \( x = -7 \) into the function

Substitute \( x = -7 \) into \( -(x + 8)^2 + 1 \):
First, calculate \( x + 8 = -7 + 8 = 1 \).
Then, square it: \( 1^2 = 1 \).
Multiply by -1: \( -1 \times 1 = -1 \).
Add 1: \( -1 + 1 = 0 \).

Answer:

\( 0 \)