Question

Fungsi f: R-R dan g: R-R ditentukan oleh rumus f(x) = x+2 dan g(x)=2x. tentukanlah rumus fungsi komposisi (fog)^-1(x) dan (gof)^-1(x)

Answer 1

Fog(x) = f(2x) = 2x+ 2
fog^-1(2x+2) = x
2x+2 = a
(x+1) = 1/2 a
x = 1/2 a - 1
(fog)^-1(a) = 1/2 a - 1
(fog)^-1(x) = 1/2 x - 1= (x-2)/2
.
gof (x) = g(x+2) = 2(x+2) = 2x+ 4
(gof)^-1 (2x+4) = x
2x + 4= a
2x = a-4
x = (a-4)2
(gof)^-1(a) = (a-4)/2
(gof)^-1(x) = (x-4)/2