Question

If $ f:R\to R $ is given by
$ f(x)=\left\{ \begin{matrix} -1,\,when\,\,x\,\,is\,\,rational \\ 1,\,when\,\,x\,\,is\,\,irrational \\ \end{matrix} \right. $
then $ (fof)\,(1-\sqrt{3}) $ is equal to

• A. $ 1 $
• B. $ -1 $
• C. $ \sqrt{3} $
• D. $ 0 $

Answer 1

Answer: (B)

Given, $ f(x)=\left\{ \begin{matrix} -1,\,where\,\,x\,\,is\,rational \\ 1,\,when\,\,x\,is\,\,irrational\, \\ \end{matrix} \right. $
Now, $ (fof)\,(1-\sqrt{3})=f[f(1-\sqrt{3})]=f(1)=-1 $