Question

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

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

Answer 1

Answer: (B)

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