If $f(x) = |x - 3|,$ then $f$ is

Let $a \in Z$ and $[t]$ be the greatest integer $\leq t$. Then the number of points,where the function $f(x) = [a + 13 \sin x], x \in (0, \pi)$ is not differentiable,is $........$.

Let $f:[-1,1] \rightarrow R$ be a function defined by $f(x)=\begin{cases} x^2 \left| \cos \left(\frac{\pi}{x}\right) \right| & \text{for } x \neq 0 \\ 0 & \text{for } x=0 \end{cases}$. The set of points where $f$ is not differentiable is

At the point $x = 1$,the given function $f(x) = \begin{cases} x^3 - 1; & 1 < x < \infty \\ x - 1; & -\infty < x \le 1 \end{cases}$ is

Let $f: R \rightarrow R$ be a function defined by $f(x)=\begin{cases} \frac{\sin(x^2)}{x} & \text{if } x \neq 0 \\ 0 & \text{if } x=0 \end{cases}$. Then,at $x=0$,$f$ is

If $f(x) = \begin{cases} A + Bx^2, & x < 1 \\ 3Ax - B + 2, & x \geqslant 1 \end{cases}$,then find $A$ and $B$ so that $f(x)$ is differentiable at $x = 1$.