Is the statement true or false? "The domain and the range of the reciprocal function are the set of all real numbers."

Is the statement true or false? "The domain and the range of the reciprocal function are the set of all real numbers."

Question
Analyzing functions
asked 2021-01-08
Is the statement true or false? "The domain and the range of the reciprocal function are the set of all real numbers."

Answers (1)

2021-01-09

False. The domain and range of the reciprocal function are all real numbers except the number 0 since \(\displaystyle{f{{\left({0}\right)}}}=\frac{{1}}{{0}}\) is undefined. If x can’t be 0, y can’t be 0 either.
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