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If f(x) is defined on [0, 1] by the rul...

If `f(x)` is defined on `[0, 1]` by the rule `f(x)={x,` if `x` is rational ,`1-x,` if `x` is rational ' then for all `x in [0,1]` ,`f(f(x))` is

A

constant

B

1+x

C

x

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Given that, `f:[0,1] to [0, 1]` be defined by
`f(x)={(x,"if x is rational"),(1-x,"if x is irrational"):}`
` :. (fof)x=f(f(x))=x`
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