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AP EAMCET2011MathematicsApplication of Derivatives

If f:[2, ) B defined by f(x)=x^2-4 x+5 is a bijection, then B is equal to

Options

  1. A[0, )
  2. B[1, )
  3. C[4, )
  4. D[5, )

Correct answer

B. [1, )

Step-by-step solution

Given, f(x)=x^2-4 x+5 On differentiating w.r.t. x , we get f^ (x)=2 x-4 Put f^ (x)=0 x=2 For x>2, f^ (x)>0 , increasing Minimum value is f(2)=4-8+5=1 B [1, )

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