Answer
$$\lim_{x \to 1 }g(x)=0$$
Work Step by Step
Please note that the graph of $g(x)$ is the graph of $f(x)$ horizontally shrunk by $2$.
To find $\lim_{x\to 1 }g(x)$, examine the graph of $g$ near $x=1$. As $x$ gets closer to $1$, the values of $g(x)$ get closer to $0$. We conclude from the graph that$$\lim_{x \to 1 }g(x)=0.$$
