Suppose that g(x)=f−1(x). If g(-15) = 0, g(0) = 4, g(3) = 9, and g(9) = 3, what is f(f(9))?
Because f(x) is the inverse of f−1(x), and g(x) = f−1(x), f(x) is the inverse of g(x). Thus, if g(15) = 0, g(0) = 4, g(3) = 9, g(9) = 3, then f(0) = 15, f(4) = 0, f(9) = 3, f(3) = 9.
Thus, f(f(9)) = f(3) = 9