jika f(x)=1/x-1, x tidak sama dengan 1, g invers (x)=1-x/x, x tidak sama dengan 0 dan h(x)= g[f(x)], maka h invers(x)

Diket :
f(x) = 1/x-1, x tidak = 1
g^-1(x) = 1-x/x, x tidak = 0
h(x) = g[f(x)]
Ditanya : h^-1(x)
Jawab :
Telah disepakati bahwa:
(g^-1)^-1(x) = g(x)
Berarti :
g^-1(x) = 1-x/x
y = 1-x/x
xy = 1-x
xy+x = 1
x(y+1) = 1
x = 1/y+1
(g^-1)^-1(x) = 1/x+1
g(x) = 1/x+1

h(x) = g[f(x)]
h(x) = g[1/x-1]
h(x) = 1/1+x-1/x-1
h(x) = x-1/x

h(x) = x-1/x
y = x-1/x
xy = x-1
xy-x = -1
x(y-1) = -1
x = -1/y-1
h^-1(x)= -1/x-1