Limits of Functions in Real Analysis

Alright, I need some guidance with the following problem. Any help would be appreciated.

Suppose $\displaystyle lim_{x\rightarrow x_{0}}f(x)=b$ and given any $\displaystyle r>0$ the set $\displaystyle f(B'_{r}(a))$ contains both poisitive and negative real numbers,show that $\displaystyle b=0$.

After I talked to some people it sounds like there may be a typo???

Possibly $\displaystyle x_{0}=a$ in this problem? Either way I'm not really sure how to show that b=0.