An often quicker method is to see if y values of the domain boundaries of the three different parts of the function match up. For example, one boundary is -1. By substitution we realise that f(-1) does not = g(-1), where f(x) = x + 4 and g(x) = x2. I think that's what Adam was trying to assert here.. except you only need to substitute the values at the domain boundaries of the separate parts of the function.. i.e -1 and 1 (assuming you know that each of those separate 'mini-functions' are continuous throughout their entire stated domains. The graphical method I stated above illustrates how this works quite well.
