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AP EAMCET2008MathematicsFunctions

If f: R C is defined by f(x)=e^ 2 i x for x R , then f is (where C denotes the set of all complex numbers)

Options

  1. Aone-one
  2. Bonto
  3. Cone-one and onto
  4. Dneither one-one nor onto

Correct answer

D. neither one-one nor onto

Step-by-step solution

Given that, f(x)=e^ 2 i x and f: R C . Function f(x) is not one-one, because after some values of x(i e, ) 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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