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Manipal MET2017MathematicsFunctions

If f(x+y)=f(x) f(y), f(3)=3, f^ (0)=11 , then f^ (3) is equal to

Options

  1. A11 e³³
  2. B33
  3. C11
  4. D33

Correct answer

B. 33

Step-by-step solution

aligned & f^ (3)= _ h 0 f(3+h)-f(3) h & = _ h 0 f(3) f(h)-f(3) h [ f(x+y)=f(x) f(y)] aligned Now, f(x+0)=f(x) f(0) f(x)[f(0)-1]=0 Either f(x)=0 or f(0)=1 aligned f^ (3) & =f(3) _ h 0 f(h)-f(0) h & =f(3) f^ (0)=f(3) 11 & =3 11=33 aligned

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