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JEE Main201911 Jan 2019Morning ShiftMathematicsFunctionsActual

Let f: R R be defined by f(x)= x 1+x² , x R . Then the range of f is

Options

  1. A[- 1 2 , 1 2 ]
  2. BR-[-1,1]
  3. CR- [- 1 2 , 1 2 ]
  4. D(-1,1)- 0

Correct answer

A. [- 1 2 , 1 2 ]

Step-by-step solution

f(x)= x 1+x² , x R Let, y= x 1+x² y x²-x+y=0 x= 1 1-4 y² 2 1-4 y² 0 1 4 y² |y| 1 2 - 1 2 y 1 2 The range of f is [- 1 2 , 1 2 ] .

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