The complete solution set of the equation $\mathrm{Sgn}\left(\frac{x^2-5x+4}{\left\{x\right\}}\right)=-1,$ where $\left\{·\right\}$ is fractional part function, is

Find the domain of the function $\mathrm{f}\left(\mathrm{x}\right)=\frac{1}{\log \left(2-\mathrm{x}\right)}+\sqrt{\mathrm{x}+1}$.

Find the domain of the function $\mathrm{f}\left(\mathrm{x}\right)=\sqrt{1-\mathrm{x}}-{\sin }^{-1}\left(\frac{2\mathrm{x}-1}{3}\right)$.

Find domain and range of following function: $y=x^3$

Find domain and range of the function $\mathrm{y}=\frac{{\mathrm{x}}^2-2\mathrm{x}+5}{{\mathrm{x}}^2+2\mathrm{x}+5}$.

Find domain and range of following functions

$y=\frac{1}{\sqrt{x^2-x}}$

For the following function, find whether it is one-one and also into or onto

$f\left(x\right)=2\tan x; \left(\pi /2, 3\pi /2\right)\to R$