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KCET2024MathematicsLimits

Let the function satisfy the equation f(x+y)=f(x) f(y) for all x, y R , where f(0) 0 . If f(5)=3 and f^ (0)=2 , then f^ (5) is

Options

  1. A6
  2. B0
  3. C3
  4. D-6

Correct answer

A. 6

Step-by-step solution

f(x+y)=f(x) f(y) Put x=0, y=5 , we get f(0+5)=f(0) f(5) f(5)[f(0)-1]=0 f(0)=1 Consider f^ (5)= _ h 0 f(5+h)-f(5) h = _ h 0 f(5) f(h)-f(5) h = _ h 0 f(5)[f(h)-1] h =f(5) _ h 0 f(h)-f(0) h =f(5) f^ (0)=2 3=6

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