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Let F be a field and b != 0 an element of F. Define the mapping \varphi:F[x]->F[x] by \varphi(f(x)) = f(bx) for every f(x) in F[x].

Let F be a field and b != 0 an element of F. Define the mapping varphi:F[x]->F[x] by varphi(f(x)) = f(bx) for every f(x) in F[x]. Prove that varphi is an automorphism of F[x] such that varphi(a) = a for every a in F.

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