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f(x)=cosx/([2x/pi]+1/2) where x is...

f(x)=`cosx/([2x/pi]+1/2)` where x is not an integral multiple of `pi` and [ . ] denotes the greatest integer function, is (a)an odd function (b)an even function (c)neither odd nor even (d)none of these

A

an odd function

B

an even function

C

neither odd nor even

D

None of these

Text Solution

Verified by Experts

`f(-x)=(cos(-x))/([-(2x)/(pi)]+(1)/(2))=(cosx)/(-1-[(2x)/(pi)]+(1)/(2))`(As x is not an integral multiple of `pi`)
`= -(cosx)/([(2x)/(pi)]+(1)/(2))= -f(x)`
Therefore, `f(x)` is an odd function.
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