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MHT CET202013 Oct 2020Morning ShiftMathematicsFunctionsActual

If f : R R , such that f(x)= e^ x +e^ -x e^ x -e^ -x , then f is

Options

  1. Aa periodic function
  2. Ban even function
  3. Can odd function
  4. Da neither even nor odd function

Correct answer

C. an odd function

Step-by-step solution

f(x)= e^ x +e^ -x e^ x -e^ -x = e^ x + 1 e^ x e^ x - 1 e^ x = e^ 2 x +1 e^ 2 x -1 f(-x)= e^ -x +e^ x e^ -x -e^ x = 1 e^ x +e^ x 1 e^ x -e^ x = 1+e^ 2 x 1-e^ 2 x = 1+e^ 2 x - (e^ 2 x -1 ) f(-x)=-f(x) f ( x ) is an odd function.

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