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Black Book Advanced Problems in MathematicsMathematicsFunctions

Let f(x) be invertible function and let f⁻¹(x) be its inverse. Let equation f(x) = f⁻¹(x) has two real roots and (with in domain of f(x) ), then :

Options

  1. Af(x) = x also have same two real roots
  2. Bf⁻¹(x) = x also have same two real roots
  3. Cf(x) = f⁻¹(x) also have same two real roots
  4. DArea of triangle formed by (0, 0), ( , f( )) , and ( , f( )) is 1 unit

Correct answer

A. f(x) = x also have same two real roots

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