g(x) =2x+3 fog (x) = 12x^2+ 32x+26, rimus f(x)?

Bab Fungsi
Matematika SMA Kelas XI

(fog) (x) = 12x² + 32x + 26
f(2x + 3) = 12x² + 32x + 26
f(2 . x/2 + 3) = 12 . (x/2)² + 32 . (x/2) + 26
f(x + 3) = 3x² + 16x + 26
f(x - 3 + 3) = 3(x - 3)² + 16(x - 3) + 26
f(x) = 3(x² - 6x + 9) + 16x - 48 + 26
f(x) = 3x² - 18x + 27 + 16x - 22
f(x) = 3x² - 2x + 5

◎◎ A ◎◎

10.) (f • g)(x) = 12x^2 + 32x + 26
g(x) = 2x + 3
Misalkan:
g(x) = a, maka
2x + 3 = a
2x = a - 3

f(g(x)) = (f • g)(x)
f(a) = 12x^2 + 32x + 26
f(a) = 3(4x^2) + 16(2x) + 26
f(a) = 3(2x)^2 + 16(2x) + 26
f(a) = 3(a - 3)^2 + 16(a - 3) + 26
f(a) = 3(a^2 -6a + 9) + 16a -48 + 26
f(a) = 3a^2 -18a + 27 + 16a -22
f(a) = 3a^2 -2a + 5
f(x) = 3x^2 -2x + 5

11.) f(x) = x+1/(2x-1)
(f•g)(x) = x+3/(2x+3)

f(g(x)) = (f•g)(x)
g(x)+1/(2g(x)-1) = x+3/(2x+3)
Kita ambil salah satu yg mengandung g(x), maka diperoleh:
g(x)+1 = x+3
g(x) = x+2
g(5) = 5+2
g(5) = 7