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
asked 2020-10-18
What tis the complete domain D and range R of the following multivariable functions: \(\displaystyle{w}{\left({x},{y}\right)}=\frac{{1}}{{{x}{\left({y}-{1}\right)}}}\)

Answers (1)

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