Question

evaluate the function. (see example 1)
( g(x)=\begin{cases}-x + 4, & \text{if } xleq -1\\3, & \text{if } -1 < x < 2\\2x - 5, & \text{if } xgeq 2end{cases} )

1. ( g(2) )

Explanation:

Step1: Determine the relevant piece of the piecewise function

We need to evaluate \( g(2) \). Looking at the domain conditions: \( x \geq 2 \) corresponds to the function \( 2x - 5 \).

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

Substitute \( x = 2 \) into \( 2x - 5 \): \( 2(2) - 5 \)

Step3: Calculate the result

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

Answer:

\( -1 \)