Question

1. fungsi komposisi (g o f)(x) = 8x^2 + 2x + 1 dan f(x) = 2x + 1,maka g(x) adalah ...
2. jika g(x) = x^2 + x - 4 dan (f o g) (x) = 4x^2 + 4x - 9 maka f(x-2) sama adalah ...

Answer 1

1) g ( f(x) ) = 8x²+2x+1
    g ( 2x+1) = 8x²+2x+1
misal --> p = 2x +1
p-1 = 2x --> x = (p-1)/2
   g( x ) = 8 ( {p-1}/2 )² + 2 ( {p-1}/2) + 1
            = 2 ( p²-2p+1) + p - 1 + 1
            = 2p²- 4p + 2 + p  =   2p²-3p+2 atau sama saja dengan 2x²-3x+2

Answer 2

1. (gof)(x)= 8x^2 + 2x + 1
    f(x) = 2x+ 1
   g(2x+1) = 8x^2 +2x +1
   2x+1 = p
x= (p-1)/2
g(x) = 8((x-1)/2)^2 + 2((x-1)/2) + 1
g(x) = 2x^2 - 3x + 2