Question

consider the following piece - wise defined function.
f(x)=\begin{cases}x^{2}+x + 7&\text{if }xlt - 5\\-5x + 7&\text{if }xgeq - 2end{cases}
step 1 of 3: evaluate this function at (x=-3). 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(-3)=quad\bigcirc\text{undefined}

Explanation:

Step1: Determine which part of the piece - wise function to use

Since $-5\leq - 3\geq - 2$, we use the second part of the function $f(x)=-5x + 7$.

Step2: Substitute $x=-3$ into the function

Substitute $x = - 3$ into $f(x)=-5x + 7$. We get $f(-3)=-5\times(-3)+7$.

Step3: Calculate the result

First, calculate $-5\times(-3)=15$. Then $15 + 7=22$.

Answer:

$22$