If $f:R \rightarrow C$ is defined by $f(x) = e^{2ix}$ for $x \in R$, then $f$ is (where $C$ denotes the set of all complex numbers)

Question

Dr. Abubacker · Accepted Answer

(d)
Given, $f(x) = e^{2ix}$ and $f:R \rightarrow C$. Function $f(x)$ is not one-one, because after some values of $x(ie,\ \pi)$ 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.

Q. If $f:R \rightarrow C$ is defined by $f(x) = e^{2ix}$ for $x \in R$, then $f$ is (where $C$ denotes the set of all complex numbers)

Explanation

Reviewed by Dr. Abubacker

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