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Let F be a field. Prove that if σ is an isomorphism of F(α1, . ....

Let F be a field. Prove that if σ is an isomorphism of F(α1, . . . , αn) with itself such that σ(αi) = αi for i = 1, . . . , n, and σ(c) = c for all c ∈ F, then σ is the identity. Conclude that if E is a field extension of F and if σ, τ : F(α1, . . . , αn) → E fix F pointwise and σ(αi) = τ (αi) for all i, then σ = τ .
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