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AP EAMCET201922 Apr 2019Morning ShiftMathematicsInverse Trigonometric FunctionsActual

The sum of the maximum and the minimum values of (2 ( ⁻¹ x )^2- ⁻¹ x+ ^2 4 ), is

Options

  1. A( ^2 8 )
  2. B( 11 ^2 8 )
  3. C( 3 ^2 2 )
  4. D(4 ^2 )

Correct answer

B. ( 11 ^2 8 )

Step-by-step solution

Given, (2 ( ⁻¹ x )^2- ⁻¹ x+ ^2 4 ) Let ( ⁻¹ x=y ) ( aligned & 2 y^2- y+ ^2 4 =2 [y^2- 2 y ]+ ^2 4 & =2 [ (y- 4 )^2- ^2 16 ]+ ^2 4 =2 (y- 4 )^2+ ^2 8 & =2 ( ⁻¹ x- 4 )^2+ ^2 8 aligned ) We know that, ( aligned 0 & ⁻¹ x - 4 ⁻¹ x- 4 3 4 0 & ( ⁻¹ x- 4 )^2 9 ^2 16 0 & 2 ( ⁻¹ x- 4 )^2 9 ^2 8 ^2 8 & 2 ( ⁻¹ x- 4 )^2+ ^2 8 5 ^2 4 & Required sum = ^2 8 + 5 ^2 4 = 11 ^2 8 aligned ) There is no option match.

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