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Question

Let f(x) be a function defined on [0, 1] such that f(x)={x, if x ϵ Q1x, if x /ϵ Q
Then, for all x ϵ [0,1],f(f(x))= 


  1. constant

  2. none of these

  3. 1+x

  4. x


Solution

The correct option is D

x


If x ϵ Q,f(x)=xf{f(x)}=f(x)=xIf x /ϵ Q,f(x)=1xf{f(x)}=f(1x)=1(1x)=xf{f(x)}=x  x ϵ [0,1]

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