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CAT 2022 Slot 2 · Quant · Functions · medium

A function is defined as f(x) = 2x+3 for x ≤ 2, and f(x) = x²−1 for x > 2. Find the value of f(f(2)).

Single correct option

A function is defined as f(x) = 2x+3 for x ≤ 2, and f(x) = x²−1 for x > 2. Find the value of f(f(2)).
  1. A. 7
  2. B. 33
  3. C. 48
  4. D. 51
Show answer and solution

Answer: (C) 48

Since 2 ≤ 2, use the first branch: f(2) = 2×2+3 = 7. Now compute f(7): since 7 > 2, use the second branch, f(7) = 7²−1 = 48. So f(f(2)) = 48. Option (a), 7, is the tempting trap answer for someone who stops after finding f(2) and forgets to apply f a second time.
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Original question written in the CAT 2022 Slot 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake