1. Tardigrade
  2. Question
  3. Mathematics
  4. The fundamental period of the function f ( x )=| cos π x |+| sin 2 π x |+ ( x /2) is [Note: y denotes the fractional part function of y]

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Q. The fundamental period of the function $f ( x )=|\cos \pi x |+|\sin 2 \pi x |+\left\{\frac{ x }{2}\right\}$, is
[Note: $\{y\}$ denotes the fractional part function of $y]$

Relations and Functions - Part 2

Solution:

Period of $|\cos \pi x |=1$
Period of $|\sin 2 \pi x|=\frac{1}{2}$
and period of $\left\{\frac{x}{2}\right\}=2$
$\therefore$ LCM of $1, \frac{1}{2}$ and 2 is 2