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?
f(f(x)) = 2(2x + 3) + 3 = 4x + 6 + 3 = 4x + 9
f(f(x)) = 2
4x + 9 = 2
4x = 2 - 9
4x = -7
x = - 7/4
Proof
f (-7/4) = 2 (-7/4) + 3 = -14/4 + 12/4 = -2/4 = -1/2
f ( f(-7/4)) = f(-1/2) = 2 (-1/2) + 3 = 2
