Which statement is correct about the function \(f:\mathbb{R}\to\mathbb{R}\), where \(f(x)=x^3-3x\)?

Correct answer: Not one-one but onto

The function is not one-one because \(f(-1)=2\) and \(f(2)=2\), although \(-1\ne2\). However, it is onto: for this continuous cubic polynomial, \(f(x)\to-\infty\) as \(x\to-\infty\) and \(f(x)\to\infty\) as \(x\to\infty\). Hence, it takes every real value. Therefore, option B is correct. Exam tip: To test one-one-ness, look for distinct inputs with the same output; for onto-ness, use continuity and end behaviour.