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AP EAMCET20228 Jul 2022Evening ShiftMathematicsFunctionsActual

The range of the function f(x)= x x^2-5 x+9 is

Options

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

Correct answer

B. [ -1 11 , 1 ]

Step-by-step solution

Given, f(x)= x x^2-5 x+9 =y (say) aligned & x^2 y-5 x y+9 y=x & x^2 y-(5 y+1) x+9 y=0 aligned For x R, D 0 aligned & b^2-4 a c 0 (5 y+1)^2-4 y(9 y) 0 & 25 y^2+10 y-36 y^2+1 0 & -11 y^2+10 y+1 0 & 11 y^2-10 y-1 0 & 11 y^2-11 y+y-1 0 & 11 y(y-1)+1(y-1) & (y-1)(11 y+1) 0 aligned Critical values of y are 1 and - 1 11 . Hence, y [- 1 11 , 1 ]

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