Domain of the function $f$,given by $f(x) = \frac{1}{\sqrt{(x - 2)(x - 5)}}$ is

If $R$ is the set of all real numbers and $f: R-\{2\} \rightarrow R$ is defined by $f(x)=\frac{2+x}{2-x}$ for $x \in R-\{2\}$, find the range of $f(x)$.

Let $f: A \rightarrow B$ be defined as $f(x) = \frac{1}{2} - \tan \left(\frac{\pi x}{2}\right)$ and $g: B \rightarrow C$ be defined as $g(x) = \sqrt{3 + 4x - 4x^2}$. If $A, B, C$ are subsets of $\mathbb{R}$ and $f$ is an onto function, then the range of the function $f(x)$ is:

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

If $[x]^2-5[x]+6=0$,where $[.]$ denotes the greatest integer function,then

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