SOLUTION: Hi, I am actually one of the tutors on this site (richard1234) and I have an algebra/analysis problem: Prove that there exists a rational function f satisfying f(x^2) = f(x)^2

Algebra ->  Rational-functions -> SOLUTION: Hi, I am actually one of the tutors on this site (richard1234) and I have an algebra/analysis problem: Prove that there exists a rational function f satisfying f(x^2) = f(x)^2      Log On


   

Question 471421: Hi, I am actually one of the tutors on this site (richard1234) and I have an algebra/analysis problem:

Prove that there exists a rational function f satisfying f(x^2) = f(x)^2 - a

if and only if a = 0 or a = 2.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Just an opinion:
if it is f%28x%5E2%29+=+%28f%28x%29%29%5E%282-a%29, the problem becomes rather routine;
but if it is f%28x%5E2%29+=+%28f%28x%29%29%5E2+-+a, then we're in for a long haul...