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AP EAMCET20227 Jul 2022Morning ShiftMathematicsFunctionsActual

The range of the function f(x)= x^2+x+1 x^2-x+1 is

Options

  1. A[ 1 3 , 3 ]
  2. B[ 1 2 , 2 ]
  3. C[ -1 2 , -1 4 ]
  4. D[ -1 2 , 2 ]

Correct answer

A. [ 1 3 , 3 ]

Step-by-step solution

Let y= x^2+x+1 x^2-x+1 aligned & y x^2-x y+y=x^2+x+1 & (y-1) x^2-(y+1) x+(y-1)=0 aligned For real x , D 0 array lc & (y+1)^2-4(y-1)^2 0 & 3 y^2-10 y+3 0 & (3 y-1)(y-3) 0 & 3 y-1 0 or y-3 0 & 3 y 1 or y 3 & y 1 3 array 1 3 y 3 i.e. y [ 1 3 , 3 ]

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