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Question

If f(x)=sin([λ] x) is a periodic function with fundamental period π, (where [.] denotes the greatest integer function), then λ belongs to

A
(2,3)
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B
[4,5)
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C
[2,3)
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D
(4,5)
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Solution

The correct option is B [4,5)
As we know that fundamental period of sinx is 2π
and fundamental period of sinax, (aR) is 2π|a|
fundamental period of
sin([λ] x)=2π[λ]
But given that fundamental period of
sin([λ] x)=π
2π[λ]=π
[λ]=4
λ[4,5)

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