<p>Match number of integers in each set with (P)0 (Q)2 (R)3 (S)less than 3 (T)more than 3</p>
domain of ln{x}
domain involving sec,floor
range of x^2-2x+2 on [0,2]
range of √(25-[x]^2)
Step-by-Step Solution
<div class="solution"><p>(A) ln{x}: {x}>0 excludes integers \to 0 integers \to (P),(S)</p><p>(B) Domain has exactly 3 admissible integers \to (R)</p><p>(C) (x-1)^2+1 on [0,2]: range [1,2], integers={1,2}: 2 \to (Q),(S)</p><p>(D) [x]\in{-5,...,5}: range values \sqrt(25-n^2) integers when n^2=0,9,16,25 \to 4+ integers \to (T)</p><p><strong>Answer: A\toP,S; B\toR; C\toQ,S; D\toT</strong></p><div class="trap-box"><strong>Trap:</strong> Don't count real values -- count only integers.<div class="key-concept"><strong>Key Concept:</strong> Integer counting in domain/range -- direct integer testing is fastest
Correct Answer: A→P,S; B→R; C→Q,S; D→T