diketahui fungsi f(x) = x - 2/x + 2 dan g(x) = x + 2. jika f^-1 menyatakan invers dari f, maka ( f o g )^-1 = ..

fungsi invers

f(x)= (x-2)/(x+2)
g(x) =  x+2

fog(x)= f { g(x)} = { g(x) - 2 } / { g(x)  + 2}
fog(x) = ( x+2-2)/(x+2+2) = (x )/(x+4)

(fog)⁻¹ (x)= (4x + 0)/(-x + 1) = 4x / (1 - x)

langsung aja yy

fof`¹(x) = x
f{ f`¹(x) = x
f`¹(x) - 2 / f`¹(x)-2 = x
f`¹(x) - 2 = x.f`¹(x) + 2x
f`¹(x) - x.f`¹(x) = 2x + 2
f`¹(x) (1 - x) = 2x + 2
f`¹(x) = 2x+2 / 1-x

gog`¹(x) = x
g{g`¹(x)} = x
g`¹(x) + 2 = x
g`¹(x) = x - 2

maka
(fog)`¹ = g`¹of`¹(x)

= g`¹{f`¹(x)}

= f`¹(x) - 2

= (2x+2) / (1-x) - 2

= 2x + 2 - 2 + 2x / 1 - x

= 4x / 1 - x

semoga berguna +_+