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$f(x) = \

$$\begin{cases} x + 6 & \\text{for } x < -5 \\\\ -5 & \\text{for } x = -5 \\\\ -(x + 5)^2 + 1 & \\text{for } x > -5 \\end{cases}$$

$
find $f(-6)$

Explanation:

Step1: Determine the applicable function

Since \(-6 < -5\), we use the first part of the piecewise function, \(f(x)=x + 6\).

Step2: Substitute \(x=-6\) into the function

Substitute \(x = -6\) into \(f(x)=x + 6\), we get \(f(-6)=-6 + 6\).

Step3: Calculate the result

\(-6+6 = 0\).

Answer:

\(0\)