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Let f: D R be a function defined by f(x)= x^2-x+c x^2+x+2 c where D is the domain of the function and R is the set of all real numbers. If f(x) is surjective, then the possible integral values of ' c ' can be:

Options

  1. A-6
  2. B-4
  3. C-2
  4. D0

Correct answer

C. -2

Step-by-step solution

Range of f(x) must be all real numbers. Hence, f(x)=1- 2 x+c x^2+x+2 c where P(x)=x^2+x+2 c For range to be R, P ( -c 2 ) < 0 c (-6,0) .

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