The domain of $f(x) = \frac{{\log_2(x + 3)}}{{x^2 + 3x + 2}}$ is

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

If $f: R \rightarrow R$ is defined by $f(x)=[2x]-2[x]$ for $x \in R$,where $[x]$ is the greatest integer not exceeding $x$,then the range of $f$ is:

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:

If $[x]^2-5[x]+6=0$,where $[\cdot]$ denotes the greatest integer function,then $x$ belongs to:

The domain of the function $\log _{10}(x^2-5x+6)$ is