diketahui fungsi f(x)= x/2x-3, x tidak sama dengan 3/2 dan g(x)=x+5 maka (gof)^-1 (x)=

Bab Fungsi

Cari (g o f)(x)
(g o f)(x)
= g(f(x))
= x/(2x - 3) + 5
= x/(2x - 3) + (5(2x - 3))/(2x - 3)
= (x + 10x - 15)/(2x - 3)
= (11x - 15)/(2x - 3)

y = (11x - 15)/(2x - 3)
y(2x - 3) = (11x - 15)
2xy - 3y = 11x - 15
15 - 3y = 11x - 2xy
15 - 3y = x(11 - 2y)
x = (15 - 3y)/(11 - 2y)
(g o f)^-1(x) = (15 - 3x)/(11 - 2x)
(g o f)^-1(x) = -(3x - 15)/-(2x - 11)
(g o f)^-1(x) = (3x - 15)/(2x - 11) dengan x tidak sama dengan 11/2

(g○f)(x) = g○(f(x))
= g○(x / (2x - 3)
= x / (2x - 3) + 5
= x / (2x - 3) + 5(2x - 3) / (2x - 3)
= (x + 10x - 15) / (2x - 3)
= (11x - 15) / (2x - 3)
y = (11x - 15) / (2x - 3)
y(2x - 3) = 11x - 15
2xy - 3y = 11x - 15
2xy - 11x = 3y - 15
x(2y - 11) = 3y - 15
x = (3y - 15) / (2y - 11)
(g○f)^-1 (x) = (3x - 15) / (2x - 11)