Maths-
General
Easy

Question

If f colon R not stretchy rightwards arrow C is defined by f left parenthesis x right parenthesis equals e to the power of 2 i x end exponent for x element of R , then f is (where C denotes the set of all complex numbers)

  1. One-one
  2. Onto
  3. One-one and onto
  4. Neither one-one nor onto

The correct answer is: Neither one-one nor onto


    Given, f left parenthesis x right parenthesis equals e to the power of 2 i x end exponent and f colon R not stretchy rightwards arrow C . Function  is not one-one, because after some values of x left parenthesis i e comma pi right parenthesis it will give the same values.
    Also, f left parenthesis x right parenthesis is not onto, because it has minimum and maximum values negative 1 minus i and 1 plus i  respectively.

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