If $f(x) = \begin{cases} x, & 0 \le x \le 1 \\ 2x - 1, & x > 1 \end{cases}$,then

If $f(x) = \begin{cases} 1 + \cos x, & x \le 0 \\ a - x, & 0 < x < 2 \\ (x - b)^2, & x \ge 2 \end{cases}$ is continuous at $x=0$ and $x=2$,then find the value of $a^2+b^2$.

Let $f:[0, \pi] \rightarrow R$ be defined as $f(x)=\begin{cases} \sin x, & \text{if } x \text{ is irrational and } x \in[0, \pi] \\ \tan^2 x, & \text{if } x \text{ is rational and } x \in[0, \pi] \end{cases}$. The number of points in $[0, \pi]$ at which the function $f$ is continuous is

Check the points where the constant function $f(x)=k$ is continuous.

If $f(x) = [x] - [\frac{x}{4}]$,$x \in R$,where $[x]$ denotes the greatest integer function,then:

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 ————