Let f(x)=3x-4x^2
Find f o f o f
So...
F(f(x))
I got a really big answer..... I think I might have done something wrong when doing the distributing algebraic work.
To find f o f(x) or f(f(x)), you need to substitute f(x) into the original function repeatedly. Let's break down the steps:
Step 1: Start with the original function f(x) = 3x - 4x^2.
Step 2: Substitute f(x) into f(x) to get f(f(x)) = f(3x - 4x^2).
Step 3: Replace x in f(x) with 3x - 4x^2 from the previous step.
f(f(x)) = 3(3x - 4x^2) - 4(3x - 4x^2)^2.
Step 4: Simplify the expression as much as possible by expanding and combining like terms.
Let's go through Step 3 in more detail:
f(f(x)) = 3(3x - 4x^2) - 4(3x - 4x^2)^2.
= 3(3x - 4x^2) - 4(3x - 4x^2)(3x - 4x^2)
= 3(3x - 4x^2) - 4(9x^2 - 24x^3 + 16x^4)
Now, distribute the multiplication:
f(f(x)) = 9x - 12x^2 - 36x^2 + 96x^3 - 64x^4.
Finally, combine like terms:
f(f(x)) = -64x^4 + 96x^3 - 48x^2 + 9x.
So the answer for f(f(x)) is -64x^4 + 96x^3 - 48x^2 + 9x.
Make sure to double-check your calculations along the way to avoid any mistakes.