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COMEDK2015MathematicsFunctions

If f(x)=e^ x and g(x)= e^ x , then which of the following is true?

Options

  1. Af g(x) g f(x)
  2. Bf g(x) =g f(x)
  3. Cf g(x) +g f(x) =0
  4. Df g(x) -g f(x) =1

Correct answer

B. f g(x) =g f(x)

Step-by-step solution

We have, f(x)=e^ x and g(x)= e^ x Now, f(g(x))=f ( e^ x )=e^ e^ x =e^ x and g(f(x))=g (e^ x )= e^ e^ x =e^ x e=e^ x Hence, f(g(x))=g(f(x)) .

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