Let h be -x, then
f(h)=f(-x),
f(f(h))=-h=x
That is, f(f(-x))=x
And because f (f (x)) =-x.
So f(f(x)) is odd function, which has a definition when x=0.
So the domain of this function is x(-R
It is easy to get that f(x) can take the value of r, that is, it is continuous on R.
Suppose a linear function passes through the origin, and then prove the hypothesis. )