The entire graph of the function f(x) is shown below (f is only defined when x is between -4 and 4 inclusive). How many values of x satisfy f(f(x)) = 2?
To find a value that satisfies f( f(x) ) = 2
let's find the inverse of both sides: f(x) = f-1(2).
To find the value of f-1(2), we need to find the x-value of the point that has a y-value of 2.
The point that has a y-value of 2 is (0,2), so the value of f-1(2) is 0.
We now have: f(x) = 0.
Again finding the inverse, we have x = f-1(0)
and the x-value that produces a y-value of 0 is -4 (because the point (-4,0) is on the graph.
This is the only solution.