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AP EAMCET20225 Jul 2022Morning ShiftMathematicsFunctionsActual

Let f: R- -1 2 R be defined by f(x)= x-2 2 x+1 . If and satisfy the equation f(f(x))=-x , then 4 ( ^2+ ^2 )=

Options

  1. A17
  2. B12
  3. C24
  4. D34

Correct answer

A. 17

Step-by-step solution

f(x)= x-2 2 x+1 f(f(x))=-x [Given] f(x)-2 2(f(x))+1 =-x x-2 2 x+1 -2 2 x-4 2 x+1 +1 =-x x-2-4 x-2 2 x-4+2 x+1 =-x -3 x-4 4 x-3 =-x 3 x+4 4 x-3 =x 3 x+4=4 x^2-3 x aligned & 4 x^2-6 x-4=0 & 2 x^2-3 x-2=0 aligned Now, + = 3 2 , =-1 Now, ( + )^2= ^2+ ^2+2 9 4 = ^2+ ^2-2 [ =-1] aligned & ^2+ ^2= 17 4 & 4 ( ^2+ ^2 )=17 aligned

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