If $f(x) = \begin{cases} x, & x \le 0 \\ 0, & x > 0 \end{cases}$ then the function $f(x)$ at $x = 0$ is:

Let $f(x) = \begin{cases} (x - 1)^{\frac{1}{2 - x}}, & x > 1, x \neq 2 \\ k, & x = 2 \end{cases}$. The value of $k$ for which $f$ is continuous at $x = 2$ is

If $f(x) = \begin{cases} \frac{81^{x}-9^{x}}{k^{x}-1} & x \neq 0 \\ 2 & x = 0 \end{cases}$ is continuous at $x = 0$,then the value of $k$ is

Suppose $f(x) = \begin{cases} a + bx, & x < 1 \\ 4, & x = 1 \\ b - ax, & x > 1 \end{cases}$ and if $\lim_{x \to 1} f(x) = f(1)$,what are the possible values of $a$ and $b$?

If the function $f(x) = \begin{cases} x + a^2\sqrt{2} \sin x, & 0 \le x < \pi/4 \\ x \cot x + b, & \pi/4 \le x < \pi/2 \\ b \sin 2x - a \cos 2x, & \pi/2 \le x \le \pi \end{cases}$ is continuous in the interval $[0, \pi]$,then the values of $(a, b)$ are:

Let $f(x) = \begin{cases} x^3+8; x < 0 \\ x^2-4; x \ge 0 \end{cases}$ and $g(x) = \begin{cases} (x-8)^{1/3}; x < 0 \\ (x+4)^{1/2}; x \ge 0 \end{cases}$. Then the number of points, where the function $g \circ f$ is discontinuous, is ————