Question

f(x)=\

$$\begin{cases}-2x + 1, & x < 1 \\\\ \\frac{2}{3}x - 3, & x \\geq 1\\end{cases}$$

evaluate f(-2)

Explanation:

Step1: Determine the applicable function part

Since \(-2 < 1\), we use the function \(f(x)= -2x + 1\) for \(x=-2\).

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

Substitute \(x=-2\) into \(f(x)= -2x + 1\), we get \(f(-2)=-2\times(-2)+1\).

Step3: Calculate the result

First, calculate \(-2\times(-2)=4\), then \(4 + 1 = 5\).

Answer:

\(5\)