Domain of $f(x) = (x^2 - 1)^{-1/2}$ is

$\left\{x \in R: \frac{2 x-1}{x^3+4 x^2+3 x} \in R\right\}$ equals

The range of the function $f : R \rightarrow R$,defined by $f(x) = \frac{(x + 1)^4}{x^4 + 1}$,is

Let the domain of the function $f(x) = \log_3 \log_5 (7 - \log_2 (x^2 - 10 x + 85)) + \sin^{-1} ( | \frac{3 x - 7}{17 - x} | )$ be $(\alpha, \beta]$. Then $\alpha + \beta$ is equal to :

If $e^x + e^{f(x)} = e$, then the domain of $f(x)$ is

The domain of the function $f(x) = \log_e(x - [x])$ is