# let f(x) be a function with the following two properties: a.) for any two real numbers x and y, f(x+y)=x+f(y).?

let f(x) be a function with the following two properties:

a.) for any two real numbers x and y, f(x+y)=x+f(y).

b.) f(0)=2. Find f(2009)

thank you

### 5 Answers

- Corben DLv 41 decade agoFavorite Answer
f(2009+0) = 2009 +f(0) = 2011.

I arrived a few seconds after michy, but I agree with him.

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- 1 decade ago
f(x+y)=x+f(y)

f(2009) = f(2009 + 0) = 2009 + f(0) = 2009 + 2 = 2011

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- 1 decade ago
Well, from what you say,

f(2009) = f(2009 + 0) = 2009 + f(0)

Looks like you can probably do the rest.

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P.S.: He-he, looks like these old fingers clack on the computer too slowly! Mr. Michy and Mr. Corben are both correct. One thing you might try to do is prove to yourself that this can only happen if f(x) = 2 + x.

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- Anonymous1 decade ago
x as in you don't have one, Or that it has somehow abondoned you? It's your ex penis, you don't hang out anymore but you can't seem to make those feelings go away

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