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Question

Let f(x)=cos(π(|x|+2[x])) where [.] represents greatest integer function, then

A
f(x) is neither odd nor even
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B
f(x) is non periodic function
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C
Range of f(x) is [-1,1]
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D
f(x) = |f(x)| for all x
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Solution

The correct option is C Range of f(x) is [-1,1]
f(x)=cos(2π[x]+π|x|)=cos(π|x|)

f(x)=f(x) hence function is even. It is also periodic function.

From graph f(x)=|f(x)| is not possible for all x.


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