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Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
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Let $f :[0,1]\rightarrow[0,1]$ be defined by$$ f(x)= \left \{ \begin{array}{1 1}\;x,if\;x\;is\;rational & \;\\1-x,if\;x\;is\;irrational & \;\end{array} \right.$$ Then $(f o f)x$ is $$\begin{array}{1 1}(A)\;constant & (B)\;1+x\\(C)\;x & (D)\;none\;of\;these\end{array}$$

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1 Answer

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  • $fof(x)=f(f(x))$
$f:[0,1] \to [0,1]$
 
$f(x)= \left\{ \begin{array}{1 1} x & \quad if\;x\;is\;rational \\ 1-x & \quad if\;x\;is\;irrational \end{array} \right. $
 
$fof(x)-f(f(x))$
 
when x is rational
 
$=f(x)$
 
=x
 
when x is irrational
 
$fof(x)=f(1-x)$
 
$=1-(1-x)$
 
$=x$
 
Hence $(fof) (x)=x$
 
'c' option is correct

 

 

answered Mar 5, 2013 by meena.p
 

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