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If f (x) = 1/(1 – x), show that f [f {f (x)}] = x. |
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Answer» Given as f (x) = 1 / (1 – x) Let us prove that the f [f {f (x)}] = x. Firstly, let us solve for the f {f (x)}. f {f (x)} = f {1/(1 – x)} = 1/1 – (1/(1 – x)) = 1/(-x/(1 – x)) = (1 – x)/-x = (x – 1)/x ∴ f {f (x)} = (x – 1)/x Then, we shall solve for the f [f {f (x)}] f [f {f (x)}] = f [(x-1)/x] = 1/[(x – (x-1))/x] = 1/[(x – x + 1)/x] = 1/(1/x) ∴ f [f {f (x)}] = x Thus proved. |
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