F(x)= x +3 dan ( g 0 f ) =2x ^2 +4x - 3 tentukan ( f 0 g )

Bab Fungsi

Misalkan
x + 3 = a
Maka
x = a - 3

(g o f)(x) = g(f(x))
2x^2 + 4x - 3 = g(x + 3)
2(a - 3)^2 + 4(a - 3) - 3 = g(a)
g(a) = 2(a^2 - 6a + 9) + 4a - 12 - 3
g(x) = 2x^2 - 12x + 9 + 4x - 15
g(x) = 2x^2 - 8x - 6

(f o g)(x)
= f(g(x))
= 2x^2 - 8x - 6 + 3
= 2x^2 - 8x - 3

f(x)=x+3, (gof)(x)=2x²+4x-3
(gof)(x)=2x²+4x-3
g(f(x))  =2x²+4x-3
g(x+3) =2x²+4x-3
misal : x+3=p
             x    =p-3 p diganti x menjadi (x-3)
g(x)      =2(x-3)²+4(x-3)-3
            =2(x²-6x+9)+4x-12-3
            =2x²-12x+18+4x-15
            =2x²-8x+3
(fog)(x)=f(g(x))
            =f(2x²-8x+3)
            =2x²-8x+3+3
            =2x²-8x+6