How would I go about doing this question:

$\displaystyle Suppose\ that\ f\ and\ g$ $\displaystyle are\ continuous\ functions\ on\ the\ closed\ interval$ $\displaystyle [0,1]\ and\ that\ 0 \leq f(x) \leq 1\ for\ every\ x\ in\ [0,1].$ $\displaystyle Show\ that\ there\ exists\ a\ real\ number$ $\displaystyle c \in [0,1]\ such\ that\ f(c)=c.$

Would you do this question using the intermediate value theorem to $\displaystyle g(x)=f(x)-x$