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  4. The period of the function f (x) 3x + 3 - [3x + 3] + sin (π x/2) , where [ x ] denotes the greatest integer le x, is

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Q. The period of the function $f (x) 3x + 3 - [3x + 3] + \sin \frac{\pi x}{2} $ , where [ x ] denotes the greatest integer $\le \, x$, is

Relations and Functions - Part 2

Solution:

$3x + 3 - [3x + 3]$ has the period $\frac{1}{3}$ and $\sin \frac{\pi x}{2}$ has the period $\frac{2 \pi}{\frac{\pi}{2}}$ i.e 4 . therefore, the period of f(x) is L.C.M. $( \frac{1}{3} , 4) = 4 $