The function $f(x) = \sin x - \cos x$ is ........

The minimum value of $|x| + |x + \frac{1}{2}| + |x - 3| + |x - \frac{5}{2}|$ is

For a real number $r$,we denote by $[r]$ the largest integer less than or equal to $r$. If $x, y$ are real numbers with $x, y \geq 1$,then which of the following statements is always true?

If $f(x) = \cos([\pi^2]x) + \cos([- \pi^2]x)$,then which of the following is true?

How many positive real numbers $x$ satisfy the equation $x^3-3|x|+2=0$?

Statement $-1$: Any function $f(x)$ is an even function if $f(-x) = f(x)$ for all $x$ in its domain.
Statement $-2$: The function $f(x) = \frac{1}{\sqrt{1 - x^2}} + \left[ \frac{x^2 + x + 1}{4} \right]$,where $[.]$ denotes the greatest integer function,is an even function.