Answer:
f(x) = (x +1)/(x -1)
Step-by-step explanation:
Let f(x) = y. We want to find y such that ...
g(y) = x
(y +1)/(y -1) = x
y +1 = xy -x . . . . . . multiply by y-1
y -xy = -x -1 . . . . . . add -1 -xy
y(x -1) = x +1 . . . . . . multiply by -1 and factor out y
y = (x +1)/(x -1) . . . . divide by the coefficient of y
Then ...
f(x) = (x +1)/(x -1)
_____
Check
g(f(x)) = ((x +1)/(x -1) +1)/((x +1)/(x -1) -1)
= ((x +1 +x -1)/(x -1)) / ((x +1 -x +1)/(x -1))
= 2x/2
= x
