Question

Determine the domains of the given rational functions. 4/((x^3)+(x^2))

Rational functions
ANSWERED
asked 2021-06-30
Determine the domains of the given rational functions.
\(\displaystyle\frac{{4}}{{{\left({x}^{{3}}\right)}+{\left({x}^{{2}}\right)}}}\)

Answers (1)

2021-07-01

By rule of the domain of the function that denominator can not be zero, we have \(\displaystyle{\left({x}^{{3}}\right)}+{\left({x}^{{2}}\right)}≠{0}\)
\(\displaystyle{\left({x}^{{3}}\right)}+{\left({x}^{{2}}\right)}={\left({x}^{{2}}\right)}{\left({x}+{1}\right)},\) that is xero for \(\displaystyle{x}^{{2}}={0}\), viz \(x=0\) and \(x+1=0, viz\ x=-1\).
So, we conclude, the domain of the given function is \(\displaystyle{R}{\left\lbrace{\left(-{1.0}\right\rbrace}\right.}\)

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