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Question

The fundamental period of the function f(x)=sin(π4[x])+tan(π2[x])+[x]+[x+13] +[x+23]3x is
[where [.]the greatest integer function ]

A
8
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B
2
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C
13
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D
Not periodic
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Solution

The correct option is A 8
Sin(π4[x]) Period = 8
tan(π2[x]) period 2
[x]+[x+13]+[x+23]=[3x]
So [3x]3x={3x} period =13
where {.} denotes the fraction part function
So, the LCM of {8,2, 13} is 8
So, the fundamental period of f is 8

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