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MHT CET202416 May 2024Morning ShiftMathematicsFunctionsActual

Range of the function f (x)= x^2+x+2 x^2+x+1 , x R is

Options

  1. A(1, 7 3 )
  2. B[1, 7 3 )
  3. C(1, 7 3 ]
  4. D[1, 7 3 ]

Correct answer

D. [1, 7 3 ]

Step-by-step solution

Let y= x^2+x+2 x^2+x+1 (y-1) x^2+(y-1) x+y-2=0 For real value of x, b^2-4 ac 0 aligned & (y-1)^2-4(y-1)(y-2) 0 & 3 y^2-10 y+7 0 & (y-1)(3 y-7) 0 & 1 y 7 3 aligned Here, y 1 for any x R R _ f = [1, 7 3 ]

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