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Functional practice (Posted on 2020-12-05) Difficulty: 3 of 5
Determine all functions f:R->R such that
f(x4-y4)+4f(xy)2=f(x4+y4)

No Solution Yet Submitted by Danish Ahmed Khan    
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re(2): No Subject | Comment 4 of 7 |
(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>

  Posted by Anne Anderson on 2024-10-30 02:03:23
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