Question

consider the following piece - wise - defined function. $f(x)=\begin{cases}x^{2}+x + 7&\text{if }x < - 5\\-5x + 7&\text{if }xgeq - 2end{cases}$ step 3 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 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. $f(-2)=square$ 〇 undefined

Explanation:

Step1: Identify the relevant part of the piece - wise function

Since \(x=-2\) and the condition \(x\geq - 2\) is met, we use \(f(x)=-5x + 7\).

Step2: Substitute \(x = - 2\) into the function

Substitute \(x=-2\) into \(f(x)=-5x + 7\), we get \(f(-2)=-5\times(-2)+7\).

Step3: Calculate the result

First, calculate \(-5\times(-2)=10\). Then \(10 + 7=17\).

Answer:

17