1.

If f (x) = (x + 1)/(x – 1), show that f [f (x)] = x.

Answer»

Given as

f(x) = (x + 1)/(x – 1)

Let us prove that the f [f (x)] = x.

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

= [(x+1)/(x-1) + 1]/[(x+1)/(x-1) – 1]

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

= [(x+1) + (x-1)]/[(x+1) – (x-1)]

= (x+1+x-1)/(x+1-x+1)

= 2x/2

= x

∴ f [f (x)] = x

Thus proved.



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