Question

If $f\left(x\right)=\left\{\begin{array}{cc}{x}^2,& \mathrm{when}x<0\\ x,& \mathrm{when}0\le x<1\\ \frac{1}{x},& \mathrm{when}x\ge 1\end{array}\right.$
find: (a) f(1/2), (b) f(−2), (c) f(1), (d) $f\left(\sqrt{3}\right)$ and (e) $f\left(\sqrt{-3}\right)$.

Answer 1

Given:
$f\left(x\right)=\left\{\begin{array}{ll}{x}^2,& \mathrm{when}x<0\\ x,& \mathrm{when}0\le x<1\\ \frac{1}{x},& \mathrm{when}x\ge 1\end{array}\right.$
Now,
(a) $f\left(\frac{1}{2}\right)=\frac{1}{2}$ [ Using f (x) = x, 0 ≤ x < 1]
(b) f ($-$2) = ( $-$ 2)² = 4
(c) $f\left(1\right)=\frac{1}{1}=1$
(d) $f\left(\sqrt{3}\right)=\frac{1}{\sqrt{3}}$
(e) $f\left(\sqrt{-3}\right)$
Since x is not defined in R, $f\left(\sqrt{-3}\right)$ does not exist.