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AP EAMCET202123 Aug 2021Evening ShiftMathematicsFunctionsActual

The range of the function f(x)=- 5-6 x-x^2 is

Options

  1. A[-2,2]
  2. B[- 14 , 0]
  3. C[2, ]
  4. D[-2,0]

Correct answer

B. [- 14 , 0]

Step-by-step solution

f(x)=- 5-6 x-x^2 Let f(x)=y aligned & y=- - (x^2+6 x-5 ) & -y= - (x^2+6 x+9-9-5 ) & -y= - (x+3)^2-14 aligned On squaring both sides, y^2=14-(x+3)^2 (x+3)^2=14-y^2 x= 14-y^2 -3 which is defined only when y [- 14 , 14 But f(x) will give only negative values. Hence, range of f(x)=[- 14 , 0]

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