Answer:

f {f (x)} = f {1/(1 – x)}

f {f (x)} = 1 / 1 – (1/(1 – x))

f {f (x)} = 1 / [(1 – x – 1)/(1 – x)]

f {f (x)} = 1 / (-x/(1 – x))

f {f (x)} = (1 – x) / -x

f {f (x)} = (x – 1) / x

∴ f {f (x)} = (x – 1) / x

f [f {f (x)}] = f [(x-1)/x]

f [f {f (x)}] = 1 / [1 – (x-1)/x]

f [f {f (x)}] = 1 / [(x – (x-1))/x]

f [f {f (x)}] = 1 / [(x – x + 1)/x]

f [f {f (x)}] = 1 / (1/x)

∴ f [f {f (x)}] = x

Thus, showed.