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Let f x = x 2 - x + 1 , ∀ x ≥ 1 2 , then the solution of the equation f x = f - 1 x is

Options

  1. Ax =1
  2. Bx = 2
  3. Cx = 1 2
  4. Dx = 3

Correct answer

A. x =1

Step-by-step solution

f ( x )   and   f − 1 ( x ) intersect only on the line y = x ∴ x 2 − x + 1 = x ⇒ x 2 − 2 x + 1 = 0 ⇒ ( x − 1 ) 2 = 0 ⇒ x = 1

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