The points at which the function $f(x) = \frac{x + 1}{x^2 + x - 12}$ is discontinuous,are

Is the function defined by $f(x) = x^{2} - \sin x + 5$ continuous at $x = \pi$?

If $f(x) = \begin{cases} x^2 + \alpha, & x \ge 0 \\ 2\sqrt{x^2 + 1} + \beta, & x < 0 \end{cases}$ is continuous at $x = 0$ and $f(\frac{1}{2}) = 2$,then $\alpha^2 + \beta^2$ is

Prove that the function $f(x)=5x-3$ is continuous at $x=0$,$x=-3$,and $x=5$.

Let $f: R \to R$ be a function defined by $f(x) = [x] \cos \left( \frac{2x - 1}{2} \pi \right)$,where $[x]$ denotes the greatest integer function. Then $f$ is:

The value of $f(0)$,so that the function $f(x) = \frac{(27 - 2x)^{1/3} - 3}{9 - 3(243 + 5x)^{1/5}}, (x \ne 0)$ is continuous,is given by