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CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity

Let f(x) = 2x − 1 for all real x. The inverse function f⁻¹(x) is:

The inverse is (x + 1)/2. Writing y = 2x − 1 and solving for x gives x = (y + 1)/2. Substituting back confirms f(f⁻¹(x)) = x. The reciprocal and sign-error options do not undo the original function.

  1. A(x − 1)/2
  2. B(x + 1)/2Correct
  3. C2x + 1
  4. D1/(2x − 1)

Explanation

Put y = 2x − 1. Then x = (y + 1)/2, so f⁻¹(x) = (x + 1)/2. Check: f(f⁻¹(x)) = 2·(x + 1)/2 − 1 = x. The option (x − 1)/2 comes from a sign error, and 1/(2x − 1) is the reciprocal, not the inverse.

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