Question

question
$f(x)=\

$$\begin{cases}-(x + 8)^2 + 4&\\text{for }x\\leq -5\\\\4&\\text{for }x\\geq 3\\end{cases}$$

$
find $f(-5)$

Explanation:

Step1: Select correct function branch

Since $x=-5$ satisfies $x \leq -5$, use $f(x) = -(x+8)^2 + 4$.

Step2: Substitute $x=-5$

$$f(-5) = -(-5+8)^2 + 4$$

Step3: Simplify inside parentheses

$$f(-5) = -(3)^2 + 4$$

Step4: Calculate square and simplify

$$f(-5) = -9 + 4$$

Step5: Compute final sum

$$f(-5) = -5$$

Answer:

$-5$