Functions
General
Grade 12
Question:
Period of f(x) = \{ x \} + \{ \frac{1}{3} x \} + \{ x + \frac{2}{3} \} is equal to (where \{ . \} denotes fractional part function)
1
\frac{2}{3}
\frac{1}{2}
\frac{1}{3}
Step-by-Step Solution
<div class="solution"><p>f has symmetry about x=2 and period 16. Reflection centres repeat every T/2=8. So also symmetric about 2+8=10 and 10+8=18. Answer: 18.</p><p><strong>Answer: (D) 18</strong></p><div class="trap-box"><strong>Trap:</strong> Don't shift by full period only. Reflection centres repeat every half-period.</div><div class="key-concept"><strong>Key Concept:</strong> Period T + symmetry about x=a → also symmetric about x=a+T/2</div></div>
Correct Answer: D