Diketahui f(x) = 2x + 5 dan g(x) = x-1/x+4. Tentukan nilai dari (fog)-1 (2)

Mapel : Matematika
Materi : Fungsi Komposisi
Kelas : 8, 10

f(x) = 2x + 5

g(x) = (x - 1) / (x + 4)

Nilak fungsi (f o g) (x)

= f(x - 1 / x + 4)

= 2[(x - 1)/(x + 4)] + 5

= (2x - 2)/(x + 4) + 5

⏩Untuk Menentukan Nilai invers,
Misalkan :

(2x - 2)/(x + 4) + 5 = y
(2x - 2)/(x + 4) = y - 5
(2x - 2) = (y - 5)(x + 4)
(2x - 2) = xy + 4y - 5x - 20
2x + 5x - xy = 4y - 20 + 2
7x - xy = 4y - 18
x(7 - y) = 4y - 18
x = (4y - 18)/(7 - y)

Maka, Nilak invers nya

(f o g) -¹(x) = (4x - 18)/(7 - x)

= [4(2) - 18] / [7 - 2]
= [8 - 18] / 5
= -10/5
= -2