Q41 / 160 · AP EAMCET 2008 · Mathematics

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
  • Correct answer
    D
    neither one-one nor onto

Solution

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.

Hence, the correct answer is option: 'D'.

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