The range of the real valued function $f(x) = \log_3(5 + 4x - x^2)$ is

The domain of the function $f(x) = \frac{1}{\sqrt{[x]^2 - 3[x] - 10}}$ is (where $[x]$ denotes the greatest integer less than or equal to $x$).

Define the real-valued function $f: R - \{0\} \rightarrow R$ defined by $f(x) = \frac{1}{x}$,where $x \in R - \{0\}$. Complete the table given below using this definition. What is the domain and range of this function?

$x$	$-2$	$-1.5$	$-1$	$-0.5$	$0.25$	$0.5$	$1$	$1.5$	$2$
$y = \frac{1}{x}$	....	....	....	....	....	....	....	....	....

The domain of the real-valued function $f(x) = \sqrt[3]{\frac{x-2}{2x^2-7x+5}} + \log(x^2-x-2)$ is

The domain of the definition of the function $f(x) = \frac{1}{4-x^2} + \log_{10}(x^3-x)$ is

Find the domain and the range of the real function $f$ defined by $f(x) = \sqrt{x-1}$.