jika f(x) = 2x-3 dan (fog)(x) = [tex] \frac{ - 9x - 1}{3x + 1} [/tex] maka tentukan [tex] {g}^{ - 1} x[/tex]

(f°g)(x) = -9x-1/3x+1
2(g(x))-3 = -9x-1/3x+1
2(g(x))=-9x-1/4x+1 +3
g(x)= -18x-2/3x+1 +3
g(x) = -18x-2+3(3x+1)/4x+1
g(x) = -18x-2+9x+3/4x+1
g(x) = -9x+1/4x+1
y = -9x+1/4x+1
3xy+y = -9x+1
3xy+9x = 1-y
x(3y+9) = 1-y
x = 1-y/3y+9
g'(x) = 1-x/3x+9

Semoga bermanfaat.. Itu kalo kalo saya gak salah hitung, kalo salah hapus saja ..

Materi : Fungsi Komposisi
Kelas : XI

f(x) = 2x - 3 dan fog(x) = -9x - 1 / 3x + 1

fog (x) = -9x - 1 / 3x + 1
2(g(x)) - 3 = -9x -1 / 3x + 1
2(g(x)) = -9x -1 / 3x + 1 + 3
2(g(x)) = -9x - 1 + 9x + 3 / 3x + 1
2(g(x)) = 2 / 3x + 1
g(x) = 2 / 3x + 1 / 2
g(x) = 1 / 3x + 1
g^-1(x) = y = 1 / 3x + 1
y(3x+1) = 1
y(3x - 1) = -1
3xy - y = -1
3xy = -1 + y
x = -1 + y / 3y
y = -1 + x / 3x → Adalah invers nya