Let f(x)=x3−2x
Require to verify whether the given function f(x) is even or odd.
Recollect the following:
A function f(x) is said to be even function if f(−x)=f(x) and
A function f(x) is said to be odd function if f(−x)=−f(x)
Now f(x)=x3−2x⇒f(−x)=(−x)3−2(−x)
⇒f(−x)=−x3+2x
⇒f(−x)=−(x3−2x)
⇒f(−x)=−f(x)
Therefore, the given function is odd function.
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