AP EAMCET · Maths · Functions
If \(f: R \rightarrow C\) is defined by \(f(x)=e^{2 i x}\) for \(x \in R\), then \(f\) is (where \(C\) denotes the set of all complex numbers)
- A one-one
- B onto
- C one-one and onto
- D neither one-one nor onto
Answer & Solution
Correct Answer
(D) neither one-one nor onto
Step-by-step Solution
Detailed explanation
Given that, \(f(x)=e^{2 i x}\) and \(f: R \rightarrow C\). Function \(f(x)\) is not one-one, because after some values of \(x(i e, \pi)\) it will give the same values. Also, \(f(x)\) is not onto, because it has minimum and maximum values \(-1-i\) and \(1+i\) respectively. Hence,…
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