Find ( f o f ) (x)

Question

Find ( f o f ) ( 3 ).

f ( x ) = x^2 - x

Answer 1

THe easy way to do it:

f(3) = 3^3 - 3 = 9 - 3 = 6

f(6) = 6^2 - 6 = 36 - 6 = 30

so f(f(3)) = f(6) = 30

optionally,The hard way to do it:

f(f(x)) =

(x^2 - x)^2 - (x^2-x)

f(f(3)) =

(3^3 - 3)^2 - (3^2 - 2) =

(9-3)^2 - (9-3) =

6^2 - 6 =

36 - 6 = 30