QuestionEvaluate $g(2)$ for the piecewise function:
$g(x)=\left\{\begin{array}{ll} -x-1, & \text { if } x \leq-3 \\ -6, & \text { if }-3<x<1 \\ 4 x+1, & \text { if } x \geq 1 \end{array}\right.$
Options: A -3, B -6, C -9, D 9

Studdy Solution

STEP 1

Assumptions1. The function $g(x)$ is defined as a piecewise function with three different expressions for different ranges of $x$ . . We need to evaluate the function $g$ when $x=$ .

STEP 2

First, we need to determine which expression to use based on the value of $x$ . Since $x=2$ , we look at the conditions for $x$ in the piecewise function.
The conditions are1. $x \leq -$
2. $- < x <1$ . $x \geq1$

STEP 3

Since $x=2$ , it falls into the third condition, $x \geq1$ . Therefore, we use the corresponding expression for this condition, which is $x+1$ .

STEP 4

Now, we substitute $x=2$ into the expression $4x+1$ .
$g(2) =4(2) +1$

STEP 5

Calculate the value of $g(2)$ .
$g(2) =4(2) +1 =8 +1 =9$ So, when $x=2$ , $g(x) =9$ .
The correct answer is D9.

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