Answer
$$\lim_{x \to 3^+ }g(x)=-2$$
Work Step by Step
Please note that the graph of $g(x)$ is the graph of $f(x)$ reflected about the $x$-axis and then vertically stretched by $2$.
To find $\lim_{x\to 3^+ }g(x)$, examine the graph of $g$ near $x=3$. As $x$ gets closer to $3$ from the right, the values of $g(x)$ get closer to $-2$. We conclude from the graph that$$\lim_{x \to 3^+ }g(x)=-2.$$
