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AP EAMCET202315 May 2023Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

The range of 1 ^2 x+3 x x+5 ^2 x is

Options

  1. A[2, 11 2 ]
  2. B[ 1 2 , 11 2 ]
  3. C[ 2 11 , 1 2 ]
  4. D[ 2 11 , 2 ]

Correct answer

D. [ 2 11 , 2 ]

Step-by-step solution

aligned & Let f(x)= 1 ^2 x+3 x x+5 ^2 x & let, g(x)= ^2 x+3 x x+5 ^2 x & =2[1+ 2 ]+1+ 3 2 2 & g(x)= 3 2 2 +2 2 +3 aligned We know the minimum and maximum value of a x+b x+c are c- a^2+b^2 and c+ a^2+b^2 respectively. Min. value of g(x)=3- ( 3 2 )^2+(2)^2 =3- 5 2 = 1 2 and max. value of g(x)=3+ ( 3 2 )^2+(2)^2 =3+ 5 2 = 11 2 Min. value of f(x)= 1 Max. value of g(x) = 1 11 2 = 2 11 Max. value of f(x)= 1 Min. value of g(x) = 1 1 2 =2 Range of f(x)= 1 ^2 x+3 x x+5 ^2 x is [ 2 11 , 2 ]

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