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Self-Reflecting Functions

CAT 1991 Slot 1 · Quantitative Ability · Medium · Algebra

This is a medium Quantitative Ability question from the CAT 1991 Slot 1 paper. It tests Algebra. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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A function can sometimes reflect on itself, i.e. if y=f(x)y = f(x), then x=f(y)x = f(y). Both of them retain the same structure and form. Which of the following functions has this property?

  1. A.

    y=2x+33x+4y = \frac{2x + 3}{3x + 4}

  2. B.

    y=2x+33x−2y = \frac{2x + 3}{3x - 2}

  3. C.

    y=3x+44x−5y = \frac{3x + 4}{4x - 5}

  4. D.

    None of the above

Answer

B

Explanation

For y=2x+33x−2y = \frac{2x + 3}{3x - 2}, solving for xx in terms of yy: y(3x−2)=2x+3  ⟹  3xy−2y=2x+3  ⟹  x(3y−2)=2y+3  ⟹  x=2y+33y−2y(3x - 2) = 2x + 3 \implies 3xy - 2y = 2x + 3 \implies x(3y - 2) = 2y + 3 \implies x = \frac{2y + 3}{3y - 2}. This has the exact same structural form f(y)f(y). Thus option (b) is correct.

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