Suppose the domain of f is (-1,1). Define the function h by h(x)=f(x)+1.What is the domain of h?

This one is pretty simple. 

Think of it like this:

You can add 1 to any domain. Read the equation more like this:

[ f(x) = h(x) ]+ 1.

Since the two domains are going to be the same no matter what that outside number is (the 1 in this case), the domain of h is (-1,1)