jika f(x)=√x;x>0 dan g(x)=x/x+1;x bukan samadengan 1 maka tentukan (gof)^-1(2)

(g o f)(x) = g(f(x))
= g(√x)
= (√x) / (√x + 1)

√x / (√x + 1) = y
√x = y √x + y
√x - y√x = y
√x (1 - y) = y
√x = y/(1 - y)
x = [y/(1 - y)]^2
(g o f)^-1(x) = [x/(1 - x)]^2
(g o f)^-1(2) = [2/(1 - 2)]^2 = [2/-1]^2 = 4

f(x) = √x
g(x) = x / (x + 1)

(gof)(x) = g{f(x)}
(gof)(x) = f(x) / (f(x) + 1)

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

(gof)`¹(x) = ( x / (1 - x) )²
(gof)`¹(2) = ( 2 / (1 - 2) )²
(gof)`¹(2) = (-2)²
(got)`¹(2) = 4

Semoga berguna +_+