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Question
Select the correct answer from given alternatives.
If f(x) =`1/(1 - x)`, then f{f[f(x)]} is
Options
x – 1
1 – x
x
– x
Solution
x
Explanation;
f[f(x)] = `"f"(1/(1 - x))`
= `1/(1 - 1/(1 - x))`
= `1/(((1 - x) - 1)/(1 - x))`
= `(x - 1)/x`
∴ f{f[f(x)]} = `"f"((x - 1)/x)`
= `1/(1 - (x - 1)/x)`
= `1/((x - (x - 1))/x`
= x
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