Let $[t]$ denote the greatest integer $\leq t$. Then the equation in $x$,$[x]^{2}+2[x+2]-7=0$ has

If $f(x) = \frac{1}{\sqrt{x+2 \sqrt{2x-4}}} + \frac{1}{\sqrt{x-2 \sqrt{2x-4}}}$ for $x > 2$, then $f(11)$ is equal to

The graphs of the polynomial $x^{2}-1$ and $\cos x$ intersect

Let $f = \{(1, 1), (2, 3), (0, -1), (-1, -3)\}$ be a linear function from $\mathbb{Z}$ into $\mathbb{Z}$. Find $f(x)$.

Let $g: (-\infty, \infty) \to (-\frac{\pi}{2}, \frac{\pi}{2})$ be defined by $g(x) = 2 \tan^{-1}(e^x) - \frac{\pi}{2}$. Then $g(x)$ is...

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.