Suppose that g(x) = f^-1(x). If g(-15) = 0, g(0) = 3, g(3) = 9, and g(9) = 20, what is f(f(9))?
Suppose that g(x) = f^-1(x). If g(-15) = 0, g(0) = 3, g(3) = 9, and g(9) = 20, what is f(f(9))?
If g(3) = 9
Then the point (3,9) is on the inverse
Then because f-1 (x) is the inverse of g
Then the point (9,3) is on f(x)
So f(9) = 3
Then f(f(9) ) = f(3)
But g (0) = 3
Then the point (0,3) is on g(x) = f-1(x)
Which means that the point (3,0) is on the graph of f(x)
So
f(f(9)) = f(3) = 0