AP EAMCET · Maths · Functions
If a function \(f: \mathrm{R} \rightarrow \mathrm{R}\) is defined by \(f(x)=x^3-x\), then \(f\) is
- A one-one and onto
- B one-one but not onto
- C onto but not one-one
- D neither one-one nor onto
Answer & Solution
Correct Answer
(C) onto but not one-one
Step-by-step Solution
Detailed explanation
Given \(f: \mathrm{R} \rightarrow \mathrm{R}\) such that \(f(x)=x^3-x=x(x-1)(x+1)\) \(\because f(1)=0=f(0)\). So, \(f(x)\) is not one-one Since, \(f(x)=x^3-x\) is a polynomial function So it is continuous on R and, If \(x \rightarrow \infty \Rightarrow f(x) \rightarrow \infty\)…
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