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For 3 , the value of f( )= ^2 + ^2 always lies in the interval

Options

  1. A(0,2)
  2. B[0,1]
  3. C(1,2)
  4. D[2, )

Correct answer

D. [2, )

Step-by-step solution

We have, f( )= ^2 + ^2 Since aligned & AM GM & ^2 + ^2 2 ( ^2 ^2 )^ 1 / 2 aligned aligned & ^2 + ^2 2 ^2 ^2 & ^2 + ^2 2 1 [ = 1 ] & ^2 + ^2 2 f( ) 2 aligned The value of f( ) always lies in the interval [2, ) .

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