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Let f(x) = x^2 + 3x - 4 . The sum of all integer values of x in the interval [-5, 5] that satisfy the equation f(|x|) = |f(x)| is

Options

  1. A15
  2. B13
  3. C6
  4. D11

Correct answer

B. 13

Step-by-step solution

The given equation is f(|x|) = |f(x)| . Substituting f(x) , we get x^2 + 3|x| - 4 = |x^2 + 3x - 4| . Case 1: x 0 Here, |x| = x , so the equation becomes x^2 + 3x - 4 = |x^2 + 3x - 4| . This is of the form A = |A| , which implies A 0 . Thus, x^2 + 3x - 4 0 (x+4)(x-1) 0 . Since x 0 , we must have x 1 . The integer solutions in [-5, 5] are 1, 2, 3, 4, 5 . Case 2: x Here, |x| = -x , so the equation becomes x^2 - 3x - 4 = |x^2 + 3x - 4| . Let A = x^2 + 3x - 4 . Subcase 2a: A 0 x^2 + 3x - 4 0 x -4 (since x Then |A| = A ,

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