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 2 of 3: evaluate this function at $x=-7$. express your answer as an integer or simplified fraction. if the function is undefined at the given value, indicate \undefined\. answer selecting a radio button will replace the entered answer value(s) with the radio button value. if the radio button is not selected, the entered answer is used. $f(-7)=square$ $\bigcirc$ undefined

Explanation:

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

Since $-7<-5$, we use $f(x)=x^{2}+x + 7$.

Step2: Substitute $x = - 7$ into the function

$f(-7)=(-7)^{2}+(-7)+7$.

Step3: Simplify the expression

First, calculate $(-7)^{2}=49$. Then $f(-7)=49-7 + 7=49$.

Answer:

$49$