Question

1. given:

$f(x)=\

$$\begin{cases} -x + 2 & -8\\leq x < -5\\\\ x^2 - 4 & -5\\leq x \\leq -2\\\\ 5 & -2 < x \\leq 10 \\end{cases}$$

$
evaluate for $x = -5$

Explanation:

Step1: Determine the applicable piece

Check the domain for \( x = -5 \). The second piece \( x^2 - 4 \) has domain \( -5 \leq x \leq -2 \), so \( x = -5 \) is in this domain.

Step2: Substitute \( x = -5 \) into the piece

Substitute \( x = -5 \) into \( x^2 - 4 \): \( (-5)^2 - 4 \)

Step3: Calculate the value

\( (-5)^2 = 25 \), so \( 25 - 4 = 21 \).

Answer:

21