Q.

Which of the following functions is an oddfunction

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a

y=x4−2x2

b

y=x−x2

c

y=cos⁡x

d

y=x−x36+x540

answer is D.

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Detailed Solution

If f(x)=x4−2x2 then f(−x)=(−x)4−2(−x)2=x4−2x2=f(x).Hence f is an even function. If u(x)=x−x2then u(−x)=x−x2 so u is neither even nor an odd functionp(x)=cbs⁡x,p(−x)=cos⁡(−x)=cos⁡x=p(x) so p is evenfunction. If s(x)=x−x36+x540 thens(−x)=−x−x36−x540=−x−x36+x540=−s(x) so s is an odd function
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