Answer
$\left\{x| x\ne0, x\ne2\right\}$
Work Step by Step
The domain of $f\circ g$ or $f(g(x))$ is the set of all $x$ such that $x$ is in the domain of $g$ and $g(x)$ is in the domain of $f$.
Since the denominator can't be equal to $0$, then $x=0$ is not in the domain of $g$.
For $f(x)$, $1x=$ is not in the domain of $f$ as it will make the denominator equal to zero..
This means that $g(x)\ne1$.
Hence,
\begin{align*}
g(x)&\ne1\\
\frac{2}{x}&\ne1\\
2&\ne x
\end{align*}
Therefore, the domain of $f\circ g$ is all real numbers except $2$ and $0$.
