Let f:D-->C(complex numbers).

Prove that if f(x)-->b as x-->a and c=/b, then there exists a delta>0, such that for any x contained in D, 0<|x-a|<delta ==> |f(x)-c|>(1/2)|b-c|.

Not really sure how to get started on this one. I'm assuming I need to find a relation between |f(x)-c| and |b-c| but I can't seem to see how to do that.