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AP EAMCET201822 Apr 2018Evening ShiftMathematicsDifferentiationActual

f: R R is a function such that f(0)=1 and for all x, y R f(x y+1)=f(x) f(y)-f(y) , -x+2 , then d f d x at x=e is

Options

  1. A0
  2. B-1
  3. Ce
  4. D1

Correct answer

D. 1

Step-by-step solution

Given functional relation is, f(x y+1)=f(x) f(y)-f(y)-x+2 Now, put y=0 , then we are getting gathered f( l )=f(x) f(0)-f(0)-x+2 f( l )=f(x)-1-x+2 f(0)=1 gathered On differentiating with respect to ' x ' 0= d f(x) d x -0-1+0 d f(x) d x =1 So, d f(x) d x ( at x=e)=1

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