JEE Mains · Maths · STD 12 - 1. relation and function
Let \(A\,=\,\{\,x\,\in \,R\,:\,x\) is not a positive int eger \(\}\) Define a function \(f\,:\,A\,\to \,R\) as \(f\,(x)\, = \frac{{2x}}{{x - 1}}\) then \(f\) is
- A injective but nor surjective
- B not injective
- C surjective but not injective
- D neither injective nor surjective
Answer & Solution
Correct Answer
(A) injective but nor surjective
Step-by-step Solution
Detailed explanation
\(f\left( x \right) = 2\left( {1 + \frac{1}{{x + 1}}} \right)\) \(f'\left( x \right) = - \frac{2}{{{{\left( {x - 1} \right)}^2}}}\) \( \Rightarrow \) \(f\) is one - one but not onto.
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