If $f(x)$ is continuous on its domain $[-2,2]$,where $f(x) = \begin{cases} \frac{\sin ax}{x} + 3, & -2 \leq x < 0 \\ 2x + 7, & 0 \leq x \leq 1 \\ \sqrt{x^2+8} - b, & 1 < x \leq 2 \end{cases}$ then the value of $2a + 3b$ is

The number of points in the interval $[2, 4]$, at which the function $f(x) = [x^2 - x - 1/2]$, where $[·]$ denotes the greatest integer function, is discontinuous, is ————

If $f(x) = \begin{cases} \frac{(8-2x)^{\frac{1}{3}} - 2}{3 - (243+5x)^{\frac{1}{5}}}, & x \neq 0 \\ k, & x = 0 \end{cases}$ is continuous at $x = 0$, then $k =$

If the function $f(x) = \begin{cases} 1+\cos x, & x \leq 0 \\ a-x, & 0 < x \leq 2 \\ x^2-b^2, & x > 2 \end{cases}$ is continuous everywhere,then $a^2+b^2=$

The values of $a$ and $b$,so that the function $f(x) = \begin{cases} x+a \sqrt{2} \sin x, & 0 \leq x \leq \frac{\pi}{4} \\ 2 x \cot x+b, & \frac{\pi}{4} < x \leq \frac{\pi}{2} \\ a \cos 2 x-b \sin x, & \frac{\pi}{2} < x \leq \pi \end{cases}$ is continuous for $0 \leq x \leq \pi$,are respectively given by

If $f(x) = \max(\sin x, \sin^{-1}(\cos x))$,then