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Question
If f(x) = `(x - 1)/(x + 1), x ≠ - 1` Show that f(f(x)) = `- 1/x`, Provided x ≠ 0
Solution
f(x) = `(x - 1)/(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)] ÷ (2x)/(x + 1)`
= `(-2)/(x + 1) xx ((x + 1))/(2x)`
= `- 2/(2x)`
= `- 1/x`
f[f(x)] = `-1/x`
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