even/odd fn.

f(x)= cosx[2xpi]+1/2

N.B - 2x/pi is in greatest integer function. nd x is not interger multiple of pi.

is this fn. even , odd, neither even nor odd ???

2 Answers

[ - x ] = - [ x ] - 1 ; where " x " is not an integer .

So , [ - 2 xÎ ] = - [ 2 xÎ ] - 1

So clearly , f ( - x ) = cos ( - x )- [ 2 xÎ ] - 1 + 12 = - { cos x[ 2 xÎ ] + 12 } = - f ( x )

Hence the function is an odd function .

thanx

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