Answer
$f(0)=2$
Work Step by Step
We are given the function:
$f(x)=x\sin\dfrac{1}{x}+2$, $x\not=0$
Graph the function:
The function is continuous on $(-\infty,0)$ and $(0,\infty)$.
We notice that close to $x=0$ the function approaches $2$, therefore in order to make it continuous in $x=0$ we must take:
$f(0)=2$
