Question

Diketahui fungsi f dan g berturut turut f(x) = 3x - 1 dan g(x) = x/x - 1, untuk x ≠ 1. rumus (f•g) pangkat -1(x) = ....
A. 2x+1/x-1, x ≠ 1
B. x+1/x-2, x ≠ 2
C. x-2/x-1, x ≠ 1
D. 3x-2/x-1, x ≠ 1
E. 2x+1/x-2, x ≠ 2

Answer 1

Fungsi Komposisi

F(x)=3x-1
G(x)=x/(x-1)

FoG⁻¹(x)=....

F⁻¹(x)=3x-1
y=3x-1
y+1=3x
(y+1)/3=x
1/3(x+1)=x

G⁻¹(x)=x/x-1
y=x/x-1
y(x-1)=x
xy-y=x
xy-x=y
x(y-1)=y
x=y/(y-1)
x=x/(x-1)

FoG⁻¹(x)=G⁻¹oF⁻¹
=G⁻¹(F⁻¹(x))
=1/3(x+1)/((1/3(x+1)-1))
=1/3(x+1)/(1/3(x)+1/3-1)
=1/3(x+1)/1/3(x)+1/3-3/3)
=1/3(x+1)/(1/3x-2/3)
=1/3(x+1)/(1/3(x-2))
-------------------- x3
=(x+1)/(x-2)

Pilihan B.

Demikian Semoga Membantu dan Bermanfaat!