(In reply to
re: No Subject by Hai Vu Nguyen)
The only solution to the functional equation is the constant function:
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mspace width="1em"></mspace><mtext>for all </mtext><mi>x</mi><mo>∈</mo><mi mathvariant="double-struck">R</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">f(x) = 0 \quad \text{for all } x \in \mathbb{R}.</annotation></semantics></math>f(x)=0for all x∈R.