Question

1. tentukan f(x) jika diketahui g(x) = 2x-3 dan (g ₀ f)(x) = 8x+7
2. tentukan f(x+3) jika diketahui g(x) = 5x-1 dan (g ₀ f)(x) = 25x²+20x-6

Answer 1

1.)
(g o f)(x) = 8x + 7
g(f(x)) = 8x + 7
2f(x) - 3 = 8x + 7
2f(x) = 8x + 10
f(x) = 4x + 5

2.)
(g o f)(x) = 25x²+20x-6
g(f(x)) = 25x²+20x-6
5f(x)-1 = 25x²+20x-6
5f(x) = 25x²+20x-5
5f(x) = 5(5x²+4x-1)
f(x) = 5x²+4x-1
Maka,
f(x+3) adalah:
= 5(x+3)²+4(x+3)-1
= 5(x²+6x+9)+4x+12-1
= 5x²+30x+45+4x+11
= 5x²+34x+56