Question

If $x$ is rational,$f\left(x\right)=1$ else $f\left(x\right)=0$. Then $fof\left(\sqrt{5}\right)=$

Answer 1

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

Consider $x=\sqrt{5}$,
$fof\left(\sqrt{5}\right)=f\left(f\right(\sqrt{5}\left)\right)$
$=f\left(0\right)\cdots \cdots \cdots [\because \sqrt{5}$ is irrational]
$=1\cdots \cdots \cdots [\because 0$ is rational]
$\therefore fof\left(\sqrt{5}\right)=1$