Find the period of following functions- fx-e cos 4- x-x-x-cos2- x

#160; f(x)=e^cos ^4π x+x [x]+cos^2π x Period of #160; cos^ 4 π x #160;is π/π i.e. 1 #160;( ∵cos (π +x)= cos x ⇒cos^4 x has pe ...

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Standard IX

Mathematics

Laws of Exponents for Real Numbers

Find the peri...

Question

Find the period of following functions: $f (x) = e^{({cos}^{4} π x + x - [x] + {cos}^{2} π x)}$

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Solution

$f (x) = e^{{cos}^{4} π x + x - [x] + {cos}^{2} π x}$
Period of ${cos}^{4} π x$ is $\frac{π}{π}$ i.e. $1$
( $∵ cos (π + x) = - cos x \Rightarrow {cos}^{4} x$ has period of $π$ )
Period of $x - [x]$ is 1.
Period of ${cos}^{2} π x$ is $\frac{π}{π}$ i.e.1
Period $=$ LCM of ${1, 1, 1}$ is $1$

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