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AP EAMCET2011MathematicsTrigonometric Ratios & Identities

If f(x)= ^6 x+ ^6 x for x R , then f(x) lies in the interval

Options

  1. A[ 7 8 , 5 4 ]
  2. B[ 1 2 , 5 8 ]
  3. C[ 1 4 , 1 ]
  4. D[ 1 4 , 1 2 ]

Correct answer

C. [ 1 4 , 1 ]

Step-by-step solution

Given, f(x)= ^6 x+ ^6 x and x R aligned & f(x)= ( ^2 x )^3+ ( ^2 x )^3 & f(x)= ( ^2 x+ ^2 x ) & ^4 x+ ^4 x- ^2 x ^2 x & & f(x)=1 ( ^2 x+ ^2 x )^2-2 ^2 x ^2 x . & .- ^2 x ^2 x & f(x)= 1-3 ^2 x ^2 x & aligned 0 ^2 x 1 array lc & 0 ( 2 x)^2 1 & 0 -3( 2 x)^2 4 -3 / 4 & 1 1- 3 4 ( 2 x)^2 1- 3 4 & 1 f(x) 1 / 4 & f(x)[1 / 4,1] x R array

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