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precalc!!!!!

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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.

  • precalc!!!!! - ,

    f(x) =3x-4x^2
    f(f(x))=3(3x-4x^2)-4(3x-4x^2)^2
    factor out (3x-4x^2)
    =(3x-4x^2)(3-4(3x-4x^2)
    =(3x-4x^2)(3-12x+16x^2)
    f(f(f(x))=3(3x-4x^2)(3-12x+16x^2)-4(3x-4x^2)(3-12x+16x^2)^2
    factor out (3x-4x^2)(3-12x+16x^2)
    f(f(f(x))=(3x-4x^2)(3-12x+16x^2)(3-4(3x-4x^2)(3-12x+16x^2))
    =(3x-4x^2)(3-12x+16x^2)(3-4(9x-36x^2+48x^3-12x^2+48x^3-64x^4)
    simplifying
    =(3x-4x^2)(3-12x+16x^2)(3-4(9x-48x^2+96x^3-64x^4)
    =(3x-4x^2)(3-12x+16x^2)(3-36x+192x^2+384x^3-256x^4)
    A really big answer

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