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If f(x)={x^2 sin((pi x)/2), |x|<1; x|x|...

If `f(x)={x^2 sin((pi x)/2), |x|<1`; `x|x|, |x|>=1` then `f(x)` is

A

an even function

B

an odd function

C

a periodic function

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`f(-x)={((-x)^(2)"sin"(pi (-x))/(2)",",|-x| lt 1),((-x)|-x|",",|-x| ge 1):},`
`={(-x^(2)"sin"(pi x)/(2)",",|x| lt 1),(-x|x|",",|x| ge 1):}`,
`= -f(x)`
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