Let $f(x) = |2x^2 + 5|x| - 3|$,$x \in R$. If $m$ and $n$ denote the number of points where $f$ is not continuous and not differentiable respectively,then $m + n$ is equal to:

If the function $g(x)=\begin{cases} K \sqrt{x+1} &, 0 \leq x \leq 3 \\ mx+2 &, 3 < x \leq 5 \end{cases}$ is differentiable, then $K+m=$

The number of points at which the function $f(x) = \max \{a-x, a+x, b\}$ for $-\infty < x < \infty$ and $0 < a < b$ is not differentiable, is

The function $f(x) = |x| + |x - 1|$ is

The domain of the derivative of the function $f(x) = \frac{x}{1+|x|}$ is

$f(x) = \begin{cases} [\cos \pi x]; & x \leqslant 1 \\ 2\{x\} - 1; & x > 1 \end{cases}$ Comment on the derivability at $x = 1$,where $[\cdot]$ denotes the greatest integer function and $\{\cdot\}$ denotes the fractional part function.