Question

Let $f\left(x\right)=\{\begin{array}{c}1;\text{if}x\text{is a rational number}\\ 0;\text{if}x\text{is an irrational number}\end{array}$. Then find the value of $f\left(f\right(\sqrt{3}\left)\right)$.

Answer 1

Given, $f\left(x\right)=\{\begin{array}{c}1;\text{if}x\text{is a rational number}\\ 0;\text{if}x\text{is an irrational number}\end{array}$.

Now $f\left(f\right(\sqrt{3}\left)\right)=f\left(0\right)=1$.

[ Since value of $f\sqrt{3}=0$ as $\sqrt{3}$ is an irrational number and value of $f\left(0\right)=1$ as $0$ is a rational number.]