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Question

Which one of the following is not a periodic function?

A
sin2x+cosx
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B
cosx
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C
tan4x
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D
logcos2x
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Solution

The correct option is B cosx
Option A, f(x)=sin2x+cosx
Period of sin2x is 2π2=π
Period of cosx is 2π
LCM of 2π and π is 2π
Option B, f(x)=cos2
Period of f(x) does not exists.
Option C, f(x)=tan4x
Period of tan4x is π4

Option D
Period of h(x)=logcos2x
Here f(x)=logx and g(x)=cos2x
So, period of f(g(x)) is same as period of g(x)
Period of cos2x is 2π2=π
Hence, period of h(x) is π

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