If f(x) = x^2 - 4 for x >= -4 and x + 3 otherwise, then for how many values of x is f(f(x)) = 5?

Answer 1

To find for how many values of x is f(f(x)) = 5, we need to find when f(x) = 5.

When x >= -4, f(x) = x^2 - 4.

Therefore, x^2 - 4 = 5
x^2 = 9
x = ±3

Therefore, for x = 3 and x = -3, f(x) = 5 when x >= -4.

When x < -4, f(x) = x + 3.

Therefore, x + 3 = 5
x = 2

Therefore, for x = 2, f(x) = 5 when x < -4.

Therefore, there are 3 values of x for which f(f(x)) = 5, which are x = 3, x = -3, and x = 2.