If $f:(-7,7) \rightarrow R$ is defined by $f(x)=[x]$ for all $x \in (-7,7)$,then the number of discontinuities of $f$ is

If $f(x) = x\sqrt{1 - [x]^2}$,then (where $[.]$ denotes the greatest integer function):

Let $f(x) = [2x^2 + 1]$ and $g(x) = \begin{cases} 2x - 3, & x < 0 \\ 2x + 3, & x \geq 0 \end{cases}$,where $[t]$ denotes the greatest integer function $\leq t$. Then,in the open interval $(-1, 1)$,the number of points where $f(g(x))$ is discontinuous is equal to:

If $f(x) = \left(\frac{2^{x}-1}{1-3^{x}}\right)$ for $x \neq 0$ is continuous at $x = 0$,then $f(0) = $

For every integer $n$,let $a_n$ and $b_n$ be real numbers. Let function $f: \mathbb{R} \rightarrow \mathbb{R}$ be given by $f(x) = \begin{cases} a_n + \sin \pi x, & \text{for } x \in [2n, 2n+1] \\ b_n + \cos \pi x, & \text{for } x \in (2n-1, 2n) \end{cases}$,for all integers $n$. If $f$ is continuous,then which of the following hold$(s)$ for all $n$?

If the function $f(x) = \begin{cases} 1 + \sin \frac{\pi x}{2}, & \text{for } -\infty < x \le 1 \\ ax + b, & \text{for } 1 < x < 3 \\ 6 \tan \frac{x\pi}{12}, & \text{for } 3 \le x < 6 \end{cases}$ is continuous in the interval $(-\infty, 6)$,then the values of $a$ and $b$ are respectively