Diberikan fungsi f(x-2)=x / (x + 5) dan f°g(x) = 2x-1 / x A. Tentukan bentuk fungsi g(x) B. Tentukan bentuk fungsi (g°f)(1/x)

Penyelesaian :

cari f(x) terlebih dahulu!

f (x-2) = x / (x+5)
f (x-2) = (x-2)+2 / (x-2)+7
maka, f (x) = x+2 / x+7

A. cari g(x)
fog (x) = f (g(x)) = 2x-1 / x
g(x)+2 / g(x)+7 = 2 - (1/x)
g(x)+2 = (g(x)+7)(2-(1/x))
g(x)+2 = 2g(x)-(1/x)g(x)+14-7(1/x)
g(x)-2g(x)+(1/x)g(x) = 14 - 2 - (7/x)
( 1-2-(1/x))g(x) = 12 - (7/x)
( -1-(1/x))g(x) = 12-(7/x)
g(x) = 12-(7/x) / ( -1-(1/x))
g(x) = (12x-7)/x / ( -x-1)/x
g(x) = (12x-7)/x . x/(-x-1)
g(x) = (12x-7) / (-x-1)
g(x) = (12x-7) / -(x+1)
g(x) = - (12x-7) / (x+1)

B. cari gof(1/x)

gof(1/x)=g(f(1/x))= g( 1/x +2 / 1/x +7)
= g( (1+2x)/x / (1+7x)/x)
= g ( 1+2x / 1+7x)
= -(12 ( 1+2x / 1+7x)-7) / ( 1+2x / 1+7x)+1
= -(12+24x/1+7x) - 7 / (1+2x+1+7x)/1+7x
= (-12-24x-7-49x)/(1+7x) . (1+7x)/(1+2x+1+7x)
= -73x-19 / 9x+2

Terima kasih.
mohon dikoreksi kalau ada kesalahan.