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Question: Answered & Verified by Expert
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)
MathematicsFunctionsTS EAMCETTS EAMCET 2008
Options:
  • A one-one
  • B onto
  • C one-one and onto
  • D neither one-one nor onto
Solution:
1191 Upvotes Verified Answer
The correct answer is: neither one-one nor onto
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, option (d) is correct.

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