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GUJCET · Maths · Relations and Functions
Function \(f: R \rightarrow R , f(x)=x^3\) is defined then, \(f\) is ____________ .
- A one-one and onto
- B many-one and onto
- C one-one but not onto
- D not one-one and onto
Answer & Solution
Correct Answer
(A) one-one and onto
Step-by-step Solution
Detailed explanation
Function is one-one since \(f(x_1)=f(x_2) \Rightarrow x_1^3=x_2^3 \Rightarrow x_1=x_2\). Function is onto since for any \(y \in R\), \(x=y^{1/3} \in R\) exists such that \(f(x)=y\).
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