Answer
The function $ f $ is continuous at $ x=2$.
Work Step by Step
Recall that if $ f $ is a polynomial function, then we have $\lim_\limits{x\to a}f(x)=f(a)$.
$\lim_\limits{x\to 2} f(x)=\lim_\limits{x\to 2} (2-x)=0$ at $ x=2$
and $\lim_\limits{x\to 2} f(x)=\lim_\limits{x\to 2} (x^2-2x)=0$ at $ x=2$
So, $\lim_\limits{x\to 2} (2-x)= \lim_\limits{x\to 2} (x^2-2x)$
Therefore, the function $ f $ is continuous at $ x=2$
