If $f(x) = \begin{cases} \frac{|x - a|}{x - a}, & x \neq a \\ 1, & x = a \end{cases}$,then:

Let $f: R \rightarrow R$ be defined as $f(x) = \begin{cases} [e^x], & x < 0 \\ a e^x + [x - 1], & 0 \leq x < 1 \\ b + [\sin(\pi x)], & 1 \leq x < 2 \\ [e^{-x}] - c, & x \geq 2 \end{cases}$ where $a, b, c \in R$ and $[t]$ denotes the greatest integer less than or equal to $t$. Then,which of the following statements is true?

Find all points of discontinuity of $f,$ where $f$ is defined by $f(x) = \begin{cases} \frac{|x|}{x}, & \text{if } x \neq 0 \\ 0, & \text{if } x = 0 \end{cases}$

Let $k$ be a non-zero real number. If $f(x) = \begin{cases} \frac{(e^x - 1)^2}{\sin (x/k) \log (1 + x/4)}, & x \neq 0 \\ 12, & x = 0 \end{cases}$ is a continuous function,then the value of $k$ is

Find all points of discontinuity of $f$,where $f$ is defined by $f(x) = \begin{cases} 2x + 3, & \text{if } x \le 2 \\ 2x - 3, & \text{if } x > 2 \end{cases}$

The function $f(x) = \frac{1 - \sin x + \cos x}{1 + \sin x + \cos x}$ is not defined at $x = \pi$. The value of $f(\pi)$,so that $f(x)$ is continuous at $x = \pi$,is