Let f : R → R be a function defined by\(\ f(x) =\begin{cases}1\,,&\q

1.	Let f : R → R be a function defined by\(\ f(x) =\begin{cases}1\,,&\quad \text{if } x \text{ is a rational number.}\\0\,, &\quad \text {if } x \text { is an irrational number.}\end {cases}\)Find (fof ) (1- \(\sqrt{3}\)) .
Answer» (fof ) (1 - \(\sqrt{3}\) ) = f { f (1 - \(\sqrt{3}\) )} = f(0) (∵ 1 - \(\sqrt{3}\) is an irrational number) = 1 (∵ 0 is rational)

Let f : R → R be a function defined by\(\ f(x) =\begin{cases}1\,,&\quad \text{if } x \text{ is a rational number.}\\0\,, &\quad \text {if } x \text { is an irrational number.}\end {cases}\)Find (fof ) (1- \(\sqrt{3}\)) .

Answer»

(fof ) (1 - \(\sqrt{3}\) ) = f { f (1 - \(\sqrt{3}\) )} = f(0) (∵ 1 - \(\sqrt{3}\) is an irrational number)

= 1 (∵ 0 is rational)