Show that the function

(i) $\mathrm{f}\left(\frac{1}{2}\right)$

Here, $x=1 / 2$, which is rational

$\therefore f(1 / 2)=1$

(ii) $\mathrm{f}(\sqrt{2})$

Here, $x=\sqrt{2}$, which is irrational

$\therefore f(\sqrt{2})=-1$

(iii) $f(\pi)$

Here, $x=\Pi$, which is irrational

$f(\pi)=-1$

(iv) $\mathrm{f}(2+\sqrt{3})$.

Here, $x=2+\sqrt{3}$, which is irrational

$\therefore f(2+\sqrt{3})=-1$

Ans. (i) 1 (ii) $-1$ (iii) $-1$ (iv) $-1$