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I'm in a calc I class where I'm faced with the question:

Suppose that f(x) is an odd function, and periodic with period 10. If f(3) = 4, find f(7) + f(5).

Unfortunately, this is not talked about in our text, which says to me I already have this knowledge but can't seem to make sense of it.

I know that an odd function has the property f(-x) = -f(x), but how does that help if I don't know f(x)?

What I was able to find thus far has been tied to more complex ideas which I don't know and we have yet to cover. It said a function is periodic if f(x + T) = f(x). Is this going in the right direction, and if so how can go about dumbing it down a tad?

Any links to info, hints towards a direction, an explanation of the type of problem this is would be appreciated.

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Hint: For what $x$ does $f(x)=f(x+10)=f(7)?$ For what $x$ does $f(x)=f(x+10)=f(5)?$ Once you have written these out, use the oddness and periodicity to find $f(7)$ and $f(5)$ - it should be quite straightforward.

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    I was sure it didn't mean that. In fact, as usual, I was overlooking the most obvious point you made. I sat here saying they equal each other forever and neglected to realize exactly what I was saying. Thanks so much for your time and patience!2012-09-26
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Hint: You correctly translated "odd function". You know $f(3)$, so you know $f(-3)$ and similarly for any couple of opposite values of the argument of $f$.
Now, $f$ is periodic of period $10$, so $f(3)=f(3-10)=f(-7)$. But then...

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    $f(3)=f(-7)=4 \longrightarrow f(7)=-f(-7)=-4$. About the rest of the exercise, as Julien said, surely $f(5)=f(-5)$ for periodicity. But also $f(5)=-f(-5)$ because the function is odd. If $f(5)$ equals a number *and* its opposite, then it's $0$.2012-09-26