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AP EAMCET202423 May 2024Morning ShiftMathematicsFunctionsActual

If A Z and the function f : A R is defined by f(x)= 1 64-(0.5)^ 24+x-x^2 then the sum of all absolute values of elements of A is

Options

  1. A36
  2. B5
  3. C25
  4. D11

Correct answer

C. 25

Step-by-step solution

f(x)= 1 64-0.5^ 24+x-x^2 For f(x) to be defined, 64-(0.5)^ 24+x-x^2 0 aligned & 1 2^ 24+x-x^2 64=2^6 1 2^ 30+x-x^2 & 0 30+x-x^2 x^2-x-30 0 & (x-6)(x+5) 0 & x (-5,6) aligned So, A= -4,-3,-2, . ., 5 Required sum =|-4|+|-3|+|-2|+ .+|4|+|5|=25

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