Question

If $\mathrm{f}:\mathrm{R}\to \mathrm{R}$ is given by $\mathrm{f}\left(\mathrm{x}\right)=\left\{\begin{array}{ll}1;& \mathrm{if}\mathrm{x}\mathrm{is}\mathrm{rational}\\ 0;& \mathrm{if}\mathrm{x}\mathrm{is}\mathrm{irrational}\end{array}\right.$. then, $\left(\mathrm{fof}\right)(\sqrt{5)}$ is

• A. $1$
• B. $-1$
• C. $\sqrt{3}$
• D. $0$

Answer 1

The correct option is A

$1$

Explanation for the correct answer:

Let, $\mathrm{x}=\sqrt{5}$

Now, $\left(\mathrm{fof}\right)\hspace{0.17em}\left(\sqrt{5}\right)$ can be written as,

$\begin{array}{rcl}\therefore \left(\mathrm{fof}\right)\left(\sqrt{5}\right)& =& \mathrm{f}\left(\mathrm{f}\right(\sqrt{5}\left)\right)\\ & =& \mathrm{f}\left(0\right)\left[\because \mathrm{f}\left(\sqrt{5}\right)\mathrm{is}\mathrm{irrationa}\mathrm{l}\right]\\ & =& 1\left[\because \mathrm{f}\left(0\right)\mathrm{is}\mathrm{rational}\right]\end{array}$

Hence, the correct answer is an option (A).