Given $f(x) = \frac{1}{2} - \tan^{-1}\left(\frac{\pi x}{2}\right)$ for $-1 < x < 1$ and $g(x) = \sqrt{3 + 4x - 4x^2}$. Find the domain of $(f + g)$.

Range of the function $f(x) = \frac{x^2 + x + 2}{x^2 + x + 1}; x \in R$ is

If $f: R \rightarrow R$ is defined as $f(x) = \frac{x^6}{x^6+2020}$,for all $x \in R$,then the range of $f$ is .......

The range of the function $f(x) = \frac{1}{\sqrt{x-[x]}}$ is

For the function $f(x) = (1 + \frac{1}{x})^x$,the domain of $f(x)$ is:

Let $D$ be the domain of the function $f(x) = \sin^{-1} \left(\log_{3x} \left(\frac{6+2 \log_3 x}{-5x}\right)\right)$. If the range of the function $g: D \rightarrow R$ defined by $g(x) = x - [x]$ (where $[x]$ is the greatest integer function) is $(\alpha, \beta)$,then $\alpha^2 + \frac{5}{\beta}$ is equal to