Let $f = \left\{ \left(x, \frac{x^2}{1+x^2} \right) : x \in R \right\}$ be a function from $R$ into $R$. Determine the range of $f$.

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

Is it true that $x = e^{\log x}$ for all real $x$?

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

If $f(x)$ is a real function defined on $[-1, 1]$,then the function $g(x) = f(5x + 4)$ is defined on the interval