SOLUTION: Let f(x) be any function and O(x) = [f(x) � f(-x)]/2 . Show that O(x) is odd. This question is really giving me a hard time. I would love it if someone could please help me.

Question 86977: Let f(x) be any function and O(x) = [f(x) � f(-x)]/2 . Show that O(x) is odd. This question is really giving me a hard time. I would love it if someone could please help me.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Let f(x) be any function and O(x) = [f(x) � f(-x)]/2 . Show that O(x) is odd.
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Condition to be "odd": O(x) has to equal -O(-x)
O(x) = [f(x) � f(-x)]/2
-O(-x) = -[f(-x)-f(--x)]/2
= -[f(-x)-f(x)]/2
= [f(x)-f(-x)]/2
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Since the required "condition" is met, O(x) is odd.
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cheers,
Stan H.
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