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

Relations and Functions - Part 2

Solution:

Given,
$f(x)=\left\{\begin{array}{ll}1 & ; \text { if } x \text { is rational } \\ 0 & ; \text { if } x \text { is irrational }\end{array}\right.$
Consider $x=\sqrt{5}$,
$($ fo $f)(\sqrt{5})=f(f(\sqrt{5}))$
$= f (0) \ldots \ldots \ldots[\because \sqrt{5}$ is irrational $]$
$=1 \ldots \ldots \ldots[\because 0$ is rational $]$
$\therefore( fof )(\sqrt{5})=1$