The correct option is B is not periodicPeriod of cos3x is 2π3 and period of sin√(3)π x is 2π√(3)π=2√(3) Since L.C.M of 2π3 and ...

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Many-One onto Function

fx=cos 3x+sin...

Question

$f (x) = cos 3 x + sin \sqrt{3} π x$

is periodic

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is not periodic

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is even

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is odd

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Solution

The correct option is B is not periodic
Period of $cos 3 x$ is $\frac{2 π}{3}$ and period of $sin \sqrt{3} π x$ is $\frac{2 π}{\sqrt{3} π} = \frac{2}{\sqrt{3}}$
Since L.C.M of $\frac{2 π}{3}$ and $\frac{2}{\sqrt{3}}$ does not exist
Therefore given function is not periodic.

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