If $f(g(a))=6,f(x)=\frac{x}{2}$, and $g(x)=\left|x^2-10\right|$, which of the following is a possible value of $a$ ?

This is a great opportunity to Plug In the Answers! Take one of the middle answer choices and plug it in for $a$, then work the problem one step at a time to see if $f(g(a))=6$. Try (B): If $a=2$, then $g(a)=\left|(2{)}^2-10\right|=|4-10|=|-6|=6$. So, $f(g(a))=f(g(2))=f(6)=\frac{6}{2}+2=3+2=5$. Since the problem states that $f(g(a))$ is supposed to equal $6,(\mathrm{B})$ is not correct. If you don't know which way to go next, just pick a direction. Try (A): If $a=$ $\sqrt{2}$, then $g(a)=\left|(\sqrt{2}{)}^2-10\right|=|2-10|=|-8|=8$. So, $f(g(a))=f(g(\sqrt{2}))=f(8)=$ $\frac{8}{2}+2=4+2=6$. Choice $(\mathrm{A})$ is correct.