Question

Diketahui f:R -->R yang ditentukan oleh g(x) =2x + 3 dan (fog) (x) = 12x^2 + 32x + 26. Tentukan f(x)...

Answer 1

Fog(x) = 12x^2 + 32x + 26
f(g(x)) = 12x^2 + 32x + 26
f(2x+3) = 12x^2 + 32x + 26

misalnya; y = 2x + 3
y - 3 = 2x
x = y - 3 / 2

Sehingga;
f (y) = 12x^2 + 32x + 26
f (y) = 12 (y-3/2)^2 + 32 (y-3/2) + 26
f (y) = 12 (y^2-6y+9/4) + (32y-96) + 26
f (y) = 12y^2-72y+108/4 + 32y-96/2 + 26/1
f (y) = 12y^2 - 72y + 108 + 64y - 192 + 104/4
f (y) = 12y^2 + 8y + 20/4
f (y) = 3y^2 + 2y + 5

f (x) = 3x^2 + 2x + 5