To find the value of the function [tex]\( g(x) \)[/tex] when [tex]\( x = 3 \)[/tex], we need to evaluate which part of the piecewise function applies based on the given value of [tex]\( x \)[/tex].
The function [tex]\( g(x) \)[/tex] is defined as follows:
[tex]\[
g(x) = \begin{cases}
3x & \text{when } x > 1 \\
-2x & \text{when } x \leq 1
\end{cases}
\][/tex]
Now, let's determine which condition [tex]\( x = 3 \)[/tex] satisfies:
- [tex]\( 3 > 1 \)[/tex] is true.
Since [tex]\( x = 3 \)[/tex] satisfies [tex]\( x > 1 \)[/tex], we use the first part of the piecewise function:
[tex]\[
g(x) = 3x
\][/tex]
Next, we substitute [tex]\( x = 3 \)[/tex] into the equation:
[tex]\[
g(3) = 3 \cdot 3
\][/tex]
Perform the multiplication:
[tex]\[
g(3) = 9
\][/tex]
Thus, the value of the function [tex]\( g(x) \)[/tex] when [tex]\( x = 3 \)[/tex] is [tex]\( 9 \)[/tex].
