prove if $\displaystyle f,g$ are cont. on $\displaystyle [a,b]$, if$\displaystyle f(a) < g(a), f(b) > g(b)$, then there is a $\displaystyle c \in [a,b]$ s.t. $\displaystyle f(c) = g(c)$.

Ok so I believe I need to prove this using the Intermediate Value Thm. Do I need to apply the IVT to f - g? If that's even a correct approach, how do I begin to do that?