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