If $[x]$ is the greatest integer function and $f(x) = \begin{cases} 2[x] - \frac{x}{|x|}, & x \neq 0 \\ 1, & x = 0 \end{cases}$ is a real-valued function, then $f$ is

Let $f: R \rightarrow R$ be defined as $f(x) = \begin{cases} [e^x], & x < 0 \\ a e^x + [x - 1], & 0 \leq x < 1 \\ b + [\sin(\pi x)], & 1 \leq x < 2 \\ [e^{-x}] - c, & x \geq 2 \end{cases}$ where $a, b, c \in R$ and $[t]$ denotes the greatest integer less than or equal to $t$. Then,which of the following statements is true?

If $f(x) = \frac{x^2 - 10x + 25}{x^2 - 7x + 10}$ for $x \neq 5$ and $f$ is continuous at $x = 5$,then $f(5) = $

If the function $f(x) = \begin{cases} \frac{\sqrt{2 + \cos x} - 1}{(\pi - x)^2}, & x \neq \pi \\ k, & x = \pi \end{cases}$ is continuous at $x = \pi$,then $k$ equals:

If the function $f(x) = \begin{cases} a|\pi - x| + 1, & x \le 5 \\ b|\pi - x| + 3, & x > 5 \end{cases}$ is continuous at $x = 5$,then the value of $a - b$ is

The function $f(x) = 2x - |x - x^2|$ is