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The function f: R R is defined by f(x)= ^2 x+ ^4 x for x R , then f(R) is equal to

Options

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

Correct answer

C. [ 3 4 , 1 ]

Step-by-step solution

We have, aligned & f(x)= ^2 x+ ^4 x=1- ^2 x+ ^4 x & =1- ^2 x (1- ^2 x )=1- ^2 x ^2 x & =1- 1 4 ^2 2 x aligned Here, 0 ^2 2 x 1 0 ^2 2 x 4 1 4 aligned & 0 - ^2 2 x 4 - 1 4 & 1 1- ^2 2 x 4 - 1 4 & 1 1- ^2 2 x 4 - 1 4 +1 & 1 1- ^2 2 x 4 3 4 & aligned Range of f= [ 3 4 , 1 ]

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