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Function Challenge (Posted on 2007-01-27) Difficulty: 4 of 5
Let F(x) be a polynomial with real coefficients. Find all functions F(x) satisfying:

F(x)*F(2x^2-1) = F(x^2)*F(2x-1)

See The Solution Submitted by atheron    
Rating: 3.5000 (2 votes)

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Some Thoughts A feasibility check | Comment 1 of 2
If the highest degree term is a.z^n, then

F(x) has a.x^n
F(2x^2-1) has a.2^n.x^2n

So the left hand side has a^2.2^n.x^3n

F(x^2) has a.x^2n
F(2x-1) has a.2^n.x^n

So the right hand side has a^2.2^n.x^3n

A priori, the problem seems possible. At least, f(x)=C for constant C, does the job.

  Posted by Federico Kereki on 2007-01-27 11:14:00
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