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State whether the following functions ar...

State whether the following functions are odd or even.
`f(x) = (sin^(4)x)/([(x)/(2)]+(1)/(2)), x in (-2, 2)`

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`f(x) = (sin^(4)x)/([(x)/(2)]+(1)/(2)), x in (-2, 2)`
Since `-2 lt x lt 2 rArr -1 lt (x)/(2) lt 1`
Here two cases arise, `-2 lt x lt 0` and `0 le x lt 2`.
In the first case `-1 lt (x)/(2) lt 1`, and `[(x)/(2)] = 0`
`f(x) = {{:((sin^(4)x)/(-1+(1)/(2)) = -2 sin^(4) x, -2 lt x lt 0),((sin^(4)x)/(0+(1)/(2)) = 2 sin^(4)x , 0 le x le 2):}`
Clearly f(x) is an odd function.
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