Explanation

(b)
Given, $f(x) = \left\{ \begin{array}{r}
\frac{2x - 3}{2x - 3},\ \ \ \ if\ x > \frac{3}{2} \\
\frac{- (2x - 3)}{2x - 3},\ \ \ if\ x < \frac{3}{2}
\end{array} \right.\$
$= \left\{ \begin{array}{r}
1,\ \ \ if\ \ \ x > \frac{3}{2} \\
- 1,\ \ \ if\ x < \frac{3}{2}
\end{array} \right.\$
Now, RHL$= \lim_{x \rightarrow \frac{3^{+}}{2}}{f(x) = \lim_{x \rightarrow \frac{3^{+}}{2}}\ 1 = 1}$
And LHL$= \lim_{x \rightarrow \frac{3^{-}}{2}}\ f(x) = \lim_{x \rightarrow \frac{3^{-}}{2}}\ ( - 1) = - 1$
$\because\ \ \ \ \$RHL$\neq$LHL
$\therefore\ \ \ f(x)$ is discontinuous at $x = \frac{3}{2}$