F(x)= 2x+1 / x-1 , x tidak boleh sama dengan 1 dan g(x)= 3x+1 . Invers fungsi (f o g) (x)

Mapel : Matematika

Kelas : 10

Bab : Fungsi Invers
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f(x) = 2x + 1/x – 1

g(x) = 3x + 1

Nilai fungsi komposi (f o g) (x)

(f o g) (x) = f(3x + 1)

(f o g) (x) = [2(3x + 1) + 1] / [(3x + 1) – 1]

(f o g) (x) = 6x + 3/3x

Misalkan :

6x + 3/3x = y

6x + 3 = 3xy

6x = 3xy – 3

6x – 3xy = -3

3xy – 6x = 3

x(3y – 6) = 3

x = 3/3y – 6

Maka, inversnya :

(f o g)-¹(x) = 3/3x – 6

(f°g)(x) = 2(3x+1)+1/3x+1-1 = 6x+2+1/3x = 6x+3/3x
(f°g)(x) = 6x+3/3x
y = 6x+3/3x
3xy = 6x+3
3xy-6x = 3
x(3y-6) = 3
x = 3/3y-6
(f°g)'(x) = 3/3x-6

Semoga bermanfaat ..