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AP EAMCET202319 May 2023Morning ShiftMathematicsLimitsActual

Let f(x)= x 1-x + 1-x x . If _ x m f(x)=5 / 2 , then set of all possible finite values of 1 and m is

Options

  1. A0,1
  2. B0, 1 3 , 2 3
  3. C0, 2 5 , 3 5
  4. D1 5 , 4 5

Correct answer

D. 1 5 , 4 5

Step-by-step solution

aligned & _ x m f(x)= _ x m x 1-x + 1-x x & 5 / 2= _ x m x+(1-x) x(1-x) = _ x m 1 x-x^2 & 5 2 = 1 m-m^2 25 m-25 m^2=4 & 25 m^2-25 m+4=0 m= 1 5 , 1 4 aligned

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