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Question # What tis the complete domain D and range R of the following multivariable functions: w(x,y)=1/(x(y-1))

Multivariable functions
ANSWERED What tis the complete domain D and range R of the following multivariable functions: $$\displaystyle{w}{\left({x},{y}\right)}=\frac{{1}}{{{x}{\left({y}-{1}\right)}}}$$ 2020-10-19
$$\displaystyle{w}{\left({x},{y}\right)}=\frac{{1}}{{{x}{\left({y}-{1}\right)}}}$$
denominator for rational function != 0ZSK
So, $$\displaystyle{x}{\left({y}−{1}\right)}\ne{0}$$
$$\displaystyle{x}\ne{0}{\quad\text{and}\quad}{\left({y}−{1}\right)}\ne{0}$$
$$\displaystyle{x}\ne{0}{\quad\text{and}\quad}{y}\ne{1}$$
Thus, $$\displaystyle{D}=\mathbb{R}^{{2}}−{\left[{0},{1}\right]}$$
The multivariable function $$\displaystyle{w}\to{0}{a}{s}{x}{\left({y}−{1}\right)}\to\infty$$
But oo is not included in the domain.
Thus, 0 is excluded from the range for $$\displaystyle{w}{\left({x},{y}\right)}.$$
Hence , $$\displaystyle{R}=\mathbb{R}−{\left[{0}\right]}$$