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

Let $f(n) = 2^{n+1}$ and $g(n) = 1 + (n+1)2^n$ for all $n \in N$. Then:

Which of the following functions is an even function?

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...

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?

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.