Need help on how to prove a function is odd.

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To prove that the function f(x) = x / (x^2 + 1) is odd, one must demonstrate that -f(x) equals f(-x) for all x in the domain. The discussion highlights confusion regarding the function's correct form and emphasizes the need to follow forum rules for homework submissions. Participants clarify that the correct interpretation of the function is crucial for proving its oddness. Evaluating f(-x) is suggested as a key step in the proof process. Understanding the definition of odd functions is essential for successfully completing this task.
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I need to prove f(x)=x/x^2+1

I'm not sure how to because I never do this with fractions and it's just messed me up. Any help is appreciated.
 
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Welcome to PF!

THis looks like homework and we have forum rules that it must be submitted using the homework template. If you look at other posts you should see how its done.

Next:

DId you write the equation correctly is it?

f(x) = (x/x^2) + 1

or is it?

f(x) = x / (x^2 + 1)

I think you meant the 2nd one, right?

Now:

What is the definition of an odd function?
 
DennyCrane said:
I need to prove f(x)=x/x^2+1

I'm not sure how to because I never do this with fractions and it's just messed me up. Any help is appreciated.

IDK why the particular form of this function is tripping you up.

To prove f(x) is odd, you must show is that -f(x) = f(-x), for all x and -x in the domain of f.

http://en.wikipedia.org/wiki/Even_and_odd_functions

What happens when you evaluate f(-x) for this function?
 

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