Let \(R_0\) be the set of all non-zero real numbers, and let \(f : R_0 \to R_0\) be defined by
\( \displaystyle f(x) = \frac{1}{x} \)
Then f is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → one-one and onto
One-one: let \(f(a) = f(b)\).
\( \displaystyle \frac{1}{a} = \frac{1}{b} \)
\(a = b\)
Onto: take any y in \(R_0\), so \(y \ne 0\). Then
\( \displaystyle x = \frac{1}{y} \)
is a non-zero real number, and \(f(x) = y\).
Hence f is one-one and onto.