Answer:

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

f [f (x)] = [(x+1)/(x-1) + 1] / [(x+1)/(x-1) – 1]

f [f (x)] = [[(x+1) + (x-1)]/(x-1)] / [[(x+1) – (x-1)]/(x-1)]

f [f (x)] = [(x+1) + (x-1)] / [(x+1) – (x-1)]

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

f [f (x)] = 2x/2

f [f (x)] = x

∴ f [f (x)] = x

Thus, showed.