(fog)(x)=4x^2+8x-3, g(x)=2x+4. berapa f'(x)=...?

(fog)(x) = [tex] 4x^{2} + 8x - 3[/tex]
f(g(x)) = [tex] 4x^{2} + 8x - 3[/tex] 
f(2x + 4) = [tex] 4x^{2} + 8x - 3[/tex]
Misalkan 2x+4 = t
2x = t - 4
x = t-4/2

f(t) = 4 ( t-4/2 )^2 - 8 ( t-4/2 ) - 3
     = 4 ( [tex] t^{2} - 8t + 16[/tex] / 2 ) -4t + 16 - 3
     = [tex]2t^{2} -16t + 32 - 4t + 13 \\ 2t^{2} - 20t + 45[/tex] 

Jadi, f(x) = 2t^{2} - 20t + 45[/tex] 

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