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

Let f : R → R be defined by f(x) = 3x − 5. Which of the following statements about f is correct?

The function f(x) = 3x − 5 on the real numbers is both one-one and onto. Equal outputs force equal inputs, and every real y has the pre-image (y + 5)/3, so it is a bijection.

  1. Af is one-one but not onto
  2. Bf is onto but not one-one
  3. Cf is both one-one and ontoCorrect
  4. Df is neither one-one nor onto

Explanation

If f(a) = f(b) then 3a − 5 = 3b − 5, so a = b, hence f is one-one. For any real y, x = (y + 5)/3 is a real number with f(x) = y, so f is onto. Option A wrongly assumes some real y has no pre-image.

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