When x is a rational number, ff ((x)) = f (1) =1; When x is an irrational number, f(f(x))=f(0)= 1.
That is, whether X is rational or irrational, f(f(x))= 1, so ① is incorrect;
Next, judge the truth values of the three propositions.
② The inverse of rational number is rational number, and the inverse of irrational number is irrational number.
∴ For any x∈R, there is f(-x)=-f(x), so ② is correct;
③ If X is a rational number, then x+T is also a rational number; If x is irrational, then x+T is irrational.
∴ According to the expression of the function, take any rational number T that is not zero, and f(x+T)=f(x) is constant for x∈R, so ③ is correct;
④ Taking x 1=-33, x2=0 and x3=33, we can get f(x 1)=0, f(x2)= 1 and f(x3)=0.
∴ A (33 33,0), B (0, 1), C (-33,0), just △ABC is an equilateral triangle, so ④ is correct.
So choose: C.