The domain of the function $y = \frac{1}{\sqrt{|x| - x}}$ is

The range of the function $f(x) = \frac{x + 2}{|x + 2|}$ is

The range of the function $y=3 \sin \left(\sqrt{\frac{\pi^{2}}{16}-x^{2}}\right)$ is

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 $(f + g)$.

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

The domain of the function $f(x) = \frac{1}{1 + e^x}$ is $[-1, 1]$. Find the range of the function.