The piecewise functions are given below as
[tex]g(x)=\begin{cases}3,x<-4 \\ 2x+4,x\ge-4\end{cases}[/tex]We were asked to evaluate when x = -2 that is, to find the value of
[tex]g(-2)[/tex]Considering the condition for
[tex]\begin{gathered} g(x)=3,x<-4 \\ \text{wont be used here because the value of x to be used is} \\ x=-2 \\ \text{and} \\ -2>-4 \end{gathered}[/tex]Considering the second function,
[tex]\begin{gathered} g(x)=2x+4,x\ge-4 \\ It\text{ is the required function because the value of x=-2 suits the parameters} \\ \text{That's where the value of x lies} \end{gathered}[/tex]Hence,
To calculate the value of
[tex]g(-2)[/tex]we will substitute the value of
[tex]x=-2[/tex]in the function below which is
[tex]g(x)=2x+4[/tex]By substitution, we will have
[tex]\begin{gathered} g(x)=2x+4 \\ g(-2)=2(-2)+4 \\ g(-2)=-4+4 \\ g(-2)=0 \end{gathered}[/tex]Therefore,
The final answer is
g(-2) = 0