Does the inverse function of the following real valued function of real variable exist ? Give reasons. $f\left(x\right)=\left|x\right|$

If a real valued function of a real variable is defined as f (x) = ${\cos }^{-1}(3x-1)$ , then the domain of the function f , is given by

Will the inverse function of the real Pulse function of the following real variable be known? give reason f(x)=|x|

Find the domain of each of the following real valued functions of real variable: $f\left(x\right)=\frac{1}{x}$

Find the domain of each of the following real valued functions of real variable: $f\left(x\right)=\frac{1}{x-7}$

Find the domain of each of the following real valued functions of real variable: $f\left(x\right)=\frac{3x-2}{x+1}$

Find the domain of each of the following real valued functions of real variable: $f\left(x\right)=\frac{2x+1}{x^2-9}$

The domain of definition of the real function f(x)=sqrt(log_(12)x^(2)) of the real variable x, is