Question:
If $f(x)=\left\{\begin{array}{cc}x^{2}, & \text { when } x<0 \\ x, & \text { when } 0 \leq x<1 \\ \frac{1}{x}, & \text { when } x \geq 1\end{array}\right.$
find: (a) $f(1 / 2)$, (b) $f(-2)$, (c) $f(1)$, (d) $f(\sqrt{3})$ and $($ e) $f(\sqrt{-3})$.
Solution:
Given:
$f(x)= \begin{cases}x^{2}, & \text { when } x<0 \\ x, & \text { when } 0 \leq x<1 \\ \frac{1}{x}, & \text { when } x \geq 1\end{cases}$
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) $f(1)=\frac{1}{1}=1$
(d) $f(\sqrt{3})=\frac{1}{\sqrt{3}}$
(e) $f(\sqrt{-3})$
Since $x$ is not defined in $R, f(\sqrt{-3})$ does not exist.