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

The value of $p$ for which the function $f(x) = \begin{cases} \frac{(4^x - 1)^3}{\sin(\frac{x}{p}) \log(1 + \frac{x^2}{3})}, & x \ne 0 \\ 12(\log 4)^3, & x = 0 \end{cases}$ is continuous at $x = 0$ is:

Discuss the continuity of the function $f$ defined by
$f(x) = \begin{cases} x + 2, & \text{if } x \le 1 \\ x - 2, & \text{if } x > 1 \end{cases}$

Let $f(x) = \begin{cases} x^{3}-x^{2}+10x-7, & x \leq 1 \\ -2x+\log_{2}(b^{2}-4), & x > 1 \end{cases}$. Then the set of all values of $b$,for which $f(x)$ has a maximum value at $x=1$,is:

The function $f(x) = \begin{cases} x, & \text{if } 0 \le x \le 1 \\ 1, & \text{if } 1 < x \le 2 \end{cases}$ is

If $f(x) = \frac{(e^{2x} - 1) \sin x^{\circ}}{x^2}, x \neq 0$ is continuous at $x = 0$,then $f(0) =$