Question

If $f\left(x\right)=\{\begin{array}{cc}x,& x\in Q\\ 1& x\notin Q\end{array}$ then $f\left(f\right(x\left)\right)$ is

• A. $x\forall x\in R$
• B. $\{\begin{array}{c}x,x\in \phi \\ 1-x,x\in Q\end{array}$
• C. $\{\begin{array}{cc}x& ,x\notin a\\ 1-x,x\in Q& \end{array}$
• D. None

Answer 1

Answer: (D)

None

Let x $\in$ Q

then f(x) = x

and f(f(x)) = f(x) = x

Let x $\notin$ Q

then f(x) = 1

and f(f(x)) = f(1) but as 1 $\in$ Q

$\therefore$ f(f(x)) = f(1) = 1