WBJEE · Maths · Functions
For the mapping \(f: \mathbb{R}-\{1\} \rightarrow \mathbb{R}-\{2\}\), given by \(f(x)=\frac{2 x}{x-1}\), which of the following is correct ?
- A \(\mathrm{f}\) is one-one but not onto
- B f is onto but not one-one
- C \(\mathrm{f}\) is neither one-one nor onto
- D \(\mathrm{f}\) is both one-one and onto
Answer & Solution
Correct Answer
(D) \(\mathrm{f}\) is both one-one and onto
Step-by-step Solution
Detailed explanation
\(f(x)=\frac{2 x}{x-1} \Rightarrow f^{\prime}(x)=\frac{-2}{(x-1)^2} < 0\) \(\therefore \mathrm{f}(\mathrm{x})\) is one-one Let, \(\mathrm{y}_1 \in \mathbb{R}-\{2\}\) and \(\mathrm{f}\left(\mathrm{x}_1\right)=\mathrm{y}_1\) Then,…
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