How Does the Function f(x) Demonstrate the Normality of a Metric Space?

[metder]

Homework Statement

Let (X, d) be a metric space and let A,B$$\subset$$X be two disjoint
closed sets. Show that X is normal by using the function
f(x)=d(x,A)/[d(X,A)+d(x,B)]

The Attempt at a Solution

I'm somewhat stuck on this. I'm guessing the proof is pretty short, but any help would be appreciated.

 

[micromass]

What is $$f^{-1}(0)$$ and $$f^{-1}(1)$$?