Diketahui fungsi f(x)=4x+3x dab g(x) =

Mapel : Matematika

Kelas : 10

Bab : Fungsi Komposisi
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→ f(x) = 4 + 3x

→ g(x) = 4x - 5/2x + 1


Ditanya → fungsi invers (f o g) (x)

Jawaban :
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(f o g) (x) = f(4x - 5)/2x + 1)

(f o g) (x) = 4 + 3(4x - 5/2x + 1)

(f o g) (x) = 4 + (12x - 15/2x + 1)

(f o g) (x) = [4(2x + 1)/(2x + 1)] + (12x - 15/2x + 1)

(f o g) (x) = [8x + 12x + 1 - 15/2x + 1]

(f o g) (x) = 20x - 14/2x + 1



Untuk menentukan inversnya,


Misalkan :

20x - 14/2x + 1 = y

20x - 14 = 2xy + y

20x - 2xy = y + 14

x (20 - 2y) = y + 14

x = (y + 14)/(20 - 2y)



Fungsi inversnya adalah :

(f o g) -¹(x) = (x + 14/20 - 2x)


→ Opsi jawaban A