Let f(x)=x^2−1. How many distinct real roots are there to f(f(f(x)))=0?
( (x^2 - 1)^2 - 1)^2 - 1 = 0
( (x^2 -1)^2 -1 )^2 = 1
(x^2 - 1)^2 - 1 = ± 1
(x^2 - 1)^2 - 1 = 1 OR (x^2 - 1)^2 - 1 = -1
(x^2 - 1)^2 = 2 or (x^2 - 1) = 0
x^2 - 1 = ±√2 or (x^2 - 1) = 0
x^2 = 1 ± √2 or x^2 - 1 = 0
x = ±(1 ±√2) or x = ± 1
check my arithmetic, should have written it out on paper first.