I guess, this can be done without plotting the graph as well.
What you do is, start breaking the points and accordingly write down the function g(f((x)).
What I mean to say is, just consider this case, x>-1, so it will easily satisfy the condition 0<=x<=4.
So g(f(x)) would be replaced by first part of f(x).
Similarly, just break down the points and accordingly redefine the function g(f(x)). Once done, now start with the given three questions, you will be able to solve it very easily.