Question

7. Diketahui fungsi f :R ----> R dan g :R ----> R dirumuskan dengan f(x) = x - 1 / x untuk x # 0 dan g( x) = x + 3 . Tentukanlah (gof(x))^-1 .

Answer 1

F(x) = (x-1)/(x)
g(x)= x + 3

gof(x)= g{f(x)}= g {(x-1)/x)}
gof(x) = (x-1)/x + 3 = (x-1 + 3x)/x = (4x-1)/(x)
y = (4x -1)/(x)
xy = 4x - 1
xy - 4x = -1
x(y-4) = - 1
x = -1/(y-4)
(gof)⁻¹(x)=  -1/(x-4) dengan  x≠ 4