If
f(x) = x^2 - 4 if x >= -4
f(x) = x + 18 otherwise
then for how many values of x is f(f(x)) = 5?
f(f(x)) f(f(x)
(x + 18)^2 - 4 = 5 (x^2 - 4) + 18 = 5
x^2 + 36x + 324 - 4 - 5 = 0 x^2 - 4 + 18 - 5 = 0
x^2 + 36x + 315 = 0 x^2 + 9 = 0
(x + 21) ( x + 15) = 0 x^2 = -9
x = -21 or x = -15 no real solutions
