f(x)=  and (f∘g)(x)=x determine g(x)

Since (f∘f-1)(x) = (f-1∘f)(x) = x,

taking g(x) = f-1(x) will fill the bill of (f∘g)(x)=x

So we find 

f-1(x)

Start with 

f(x) = 

Replace f(x) by y

y = 

Interchange x and y

x = 

Solve for y

Multiply both sides by (y+1)

x(y+1) = 1

xy + x = 1

Isolate the term in y

xy = 1 - x

Divide bith sides by x

y = 

Replace y by f-1(x)

f-1(x) = 

That will do for g(x), so 

g(x) = 

Edwin