But it isn't necessarily negative. If f(x) = 1, then the minimum value of g is is 0, or if f(x) = 1/3 + 2x/3 then the minimum value of g is 0 again. And they show that there's a fixed point, but I don't know how to show that g has a root for all functions f. Thanks.
This is a question from the exam for the calculus class I took last semester:
It looks like it might be able to be done with squeeze theorem, but I can't work it out. Please help me with this, before I descend into madness.