If $f(x-2)=x$ for all real numbers x, then what is $f(x)$?

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If $f(x-2)=x$ for all real numbers x, then $f(x)=?$ I think the answer stays the same, because the given says for all real x. so is $f(x)=x$ or i am wrong?

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$$f(x) = f(x + 2 - 2) = x + 2.$$