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Identify the given functions whether odd...

Identify the given functions whether odd or even or neither: `f(x)={(x|x| ,, xlt=-1),([x+1]+[1-x] ,, -1lt x lt1),(-x|x| ,, xgt=1):}`

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The correct Answer is:
even
`f(-x)={(-x|-x|",",-x le -1),([-x+1]+[1+x]",",-1 lt -x lt 1),(-x(-x)|-x|",",-x ge 1):}`
`={(-x|x|",",x ge 1),([1-x]+[1+x]",",-1 lt x lt 1),(x|x|",",x le -1):}`
`=f(x)`
Hence, the function is even.
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