Question

$f\left(x\right)=1$, if $x$ is rational and $f\left(x\right)=0$, if $x$ is irrational
then $\left(fof\right)\left(\sqrt{5}\right)=$

• A. $0$
• B. $1$
• C. $\sqrt{5}$
• D. $\frac{1}{\sqrt{5}}$

Answer 1

The correct option is B $1$

Given,

$f\left(x\right)=\{\begin{array}{cc}1& \text{; if x is rational}\\ 0& \text{; if x is irrational}\end{array}$

Consider $x=\sqrt{5}$,

$\text{(f o f)}\left(\sqrt{5}\right)=f\left(f\right(\sqrt{5}\left)\right)$

$=f\left(0\right)$ .......... $[\because \sqrt{5}$ is irrational$]$

$=1$ .......... $[\because 0$ is rational$]$

$\therefore \text{(f o f)}\left(\sqrt{5}\right)=1$
Hence, option B is correct.