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))?

Guest Oct 1, 2019

#1**+2 **

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

CPhill Oct 2, 2019