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. )