\(\displaystyle{w}{\left({x},{y}\right)}=\frac{{1}}{{{x}{\left({y}-{1}\right)}}}\)

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 , \(\displaystyle{R}=\mathbb{R}−{\left[{0}\right]}\)

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 , \(\displaystyle{R}=\mathbb{R}−{\left[{0}\right]}\)