The Question does not seem to be put properly. If we denote f(f(x) say by g(x) then g(x) =x represents a straight line going through the origin, as depicted in red in the figure below and the given function f(x) represents a graph looking like the one shown in black.

Hence the two will meet at only two points, that means the two functions will meet only for two values of x and not all x.

In fact since f(f(x)) =x, it means f is the inverse of function f(x). For the given f(x), its inverse f will be as shown below