Answer
$$(f \circ g)(x)= ( \sqrt{x})^2-5=x-5$$
$$\lim_{x \to 2 }(f \circ g)(x)=-3$$
Work Step by Step
To find $\lim_{x\to 2 }(f \circ g)(x)$, examine the graph of $f \circ g$ near $x=2$. As $x$ gets closer to $2$, the values of $(f \circ g)(x)$ get closer to $-3$. We conclude from the graph that$$\lim_{x \to 2 }(f \circ g)(x)=-3.$$
