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If f(x) is definedon [0,1] by rule   f(x)={ x,       if x is rational          1-x,    if x is irrational   }  the for all x belonging to [0,1] f(f(x)) A)constant  B)1+x C)x D)none of these  
Asked by g_archanasharma | 08 Apr, 2019, 05:11: AM
answered-by-expert Expert Answer
F o r space x element of left square bracket 0 comma 1 right square bracket I f space x space i s space r a t i o n a l space rightwards double arrow f left parenthesis f left parenthesis x right parenthesis right parenthesis equals f left parenthesis x right parenthesis equals x I f space x space i s space i r r a t i o n a l rightwards double arrow f left parenthesis f left parenthesis x right parenthesis right parenthesis equals f left parenthesis 1 minus x right parenthesis S i n c e comma space x space i s space i r r a t i o n a l space s o space 1 minus x space i s space i r r a t i o n a l rightwards double arrow f left parenthesis f left parenthesis x right parenthesis right parenthesis equals f left parenthesis 1 minus x right parenthesis equals 1 minus left parenthesis 1 minus x right parenthesis equals x H e n c e comma space f left parenthesis f left parenthesis x right parenthesis right parenthesis equals x space f o r space x element of left square bracket 0 comma 1 right square bracket
Answered by Renu Varma | 08 Apr, 2019, 10:16: AM

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