Assume $f\colon\mathbb{R}\to\mathbb{R}$ satisfies $f(x-f(x))=f(x)$ and:
1) has the intermediate value property
or
2) is continuous.
Does $f$ have to be constant?
property of functions satisfying $f(x-f(x))=f(x)$
2
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real-analysis
continuity
functional-equations
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1If $f(x)$ is bijective, then $f(x)=c$ is the only possible case. – 2017-02-05
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0@mathbeing Pretty sure $f(x)=c$... (you spelled my username wrong, so it didn't ping) – 2017-02-05
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2"If $f(x)$ is bijective then $f(x) = c$" But $f(x) = c$ is not bijective so I guess what you are saying is that there cannot be any bijective solution? – 2017-02-05
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0@Winther :O Wow, I guess I'm smarter than I thought – 2017-02-05
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2See [this answer](http://math.stackexchange.com/a/327848/147873) which works with the same functional equation. – 2017-02-05