Hello,
If f and g are continuous, then the proof is trivial, since for any continuous function h, is a closed set.
And here, you have ...
Suppose f:[a,b]--> R and g:[a,b]-->R. Let T={x:f(x)=g(x)}
Prove that T is closed.
So we can set h(x)=f(x)-g(x) and then T is the set such that h(x)=0 and so T complement is the set with h(x)=/=0 and then if we can show that this is open, then it's complement, T is closed. I don't know how to show it is open though. We need to show there is some neighborhood, but I don't know what to do. Thanks.