Explanation

(a)
Given, $f(x) = x + |x|$
$\therefore\ \ \ \ f(x) = \left\{ \begin{array}{r}
2x,\ \ \ \ x \geq 0 \\
0,\ \ x < 0
\end{array} \right.\$
[image:5_image5.emf]
It is clear from the graph of $f(x)$ is continuous for every value of $x$
Alternate
Since, $x$ and $|x|$ is continuous for every value of $x$, so their sum is also continous for every value of $x$