The equation $6^{x}+8^{x}=10^{x}$ has

For a real number $x$,let $[x]$ denote the greatest integer less than or equal to $x$,and let $\{x\} = x - [x]$. The number of solutions $x$ to the equation $[x]\{x\} = 5$ with $0 \leq x \leq 2015$ is

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

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?

Let $f(x) = 2x^{2} - x - 1$ and $S = \{n \in \mathbb{Z} : |f(n)| \leq 800\}$. Then the value of $\sum_{n \in S} f(n)$ is:

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