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CAT 2020 Slot 3 · Quant · Functions · medium

A function h satisfies h(x) + 4h(1/x) = 3x + 5 for every non-zero real x. What is h(2)?

Single correct option

A function h satisfies h(x) + 4h(1/x) = 3x + 5 for every non-zero real x. What is h(2)?
  1. A. −1
  2. B. 1
  3. C. 2
  4. D. 5/2
Show answer and solution

Answer: (B) 1

Put x = 2: h(2) + 4h(1/2) = 11 … (i)
Put x = 1/2: h(1/2) + 4h(2) = 3/2 + 5 = 13/2 … (ii)

From (ii), h(1/2) = 13/2 − 4h(2). Substituting into (i): h(2) + 4(13/2 − 4h(2)) = 11 → h(2) + 26 − 16h(2) = 11 → −15h(2) = −15 → h(2) = 1.

Check: h(1/2) = 13/2 − 4 = 5/2; then 1 + 4(5/2) = 1 + 10 = 11 ✓.

Tip: Functional equations pairing x with 1/x are solved by writing the equation twice and eliminating.
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Original question written in the CAT 2020 Slot 3 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake