Question

consider the following piece - wise - defined function.
f(x)=\begin{cases}-x + 6&\text{if }xleq - 2\\4x - 7&\text{if }x > - 2end{cases}
step 1 of 3: evaluate this function at (x=-2). express your answer as an integer or simplified fraction. if the function is undefined at the given value, indicate “undefined”.
answer
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f(-2)=squarequad\text{undefined}

Explanation:

Step1: Identify the relevant part of the function

Since $x=-2$ and the condition $x\leq - 2$ corresponds to $f(x)=-x + 6$, we use this part of the piece - wise function.

Step2: Substitute $x = - 2$ into the function

Substitute $x=-2$ into $f(x)=-x + 6$. So $f(-2)=-(-2)+6$.

Step3: Simplify the expression

$f(-2)=2 + 6=8$.

Answer:

$8$