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AP EAMCET202316 May 2023Evening ShiftMathematicsFunctionsActual

Let A R , B R and f : A B be defined by f ( x )= x ^2-3 x +2 . If f is a bijection, then

Options

  1. AA=(- , 0], B= (- , -1 4 ]
  2. BA = (- , 3 2 ], B = [ -1 4 , )
  3. CA = [ 3 2 , ), B = (- , -1 4 ]
  4. DA=(- , ), B= [ -1 4 , )

Correct answer

B. A = (- , 3 2 ], B = [ -1 4 , )

Step-by-step solution

The function f defined f: A B by f(x)=x^2-3 x+2 Now f ^ ( x )=2 x -3 For stationary point, f ^ ( x )=0 x = 3 2 f ( 3 2 )= 9 4 - 9 2 +2= 9-18+8 4 = -1 4 so for one-one x [ 3 2 , ) and y [- 1 4 , ) or x (- , 3 2 ] and y [- 1 4 , )

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