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CBSE XII
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Math
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Relations and Functions
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Q)
Given a function $f:R_* \rightarrow R_*$ defined by $f(x)=\frac{1}{x}$, where $R_*$ is the set of all non-zero real numbers. Which of the following is true?
A) $f$ is one-one only
B) $f$ is onto only
C) $f$ is many-one and onto
D) $f$ is one-one and onto
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Show that the function \(f : R_* \rightarrow R_* \) defined by \( f(x) = (\frac{1} {x})\) is one-one and onto, where \(R_* \) is the set of all non-zero real numbers. Is the result true, if the domain \(R_* \) is replaced by \(N\) with co-domain being same as \(R_*\)?
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