Grades 11-12 Video Solutions 2013-Levels 11&12 Video Solutions 2013 problem22

Levels 11&12 Video Solutions 2013 problem22

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Video Summary

The function \( f \) is periodic with a period of 5, and its behavior in the interval \([-2, 3)\) is \( f(x) = x^2 \). To find \( f(2013) \), we calculate its equivalent value within this interval due to the periodic nature. By expressing 2013 as 2010 + 3 (5 × 402 + 3), it's equivalent to determining \( f(3) \). However, since 3 is not included in the interval, we use x = -2. Thus, \( f(2013) = f(-2) = (-2)^2 = 4 \). The answer is 4.

Keywords

periodic function

interval

equivalent value

period

calculation