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The Hermitian conjugate A^† of a linear operator can be defined by ⟨ψ|Aφ⟩ = ⟨A^†ψ|φ⟩ . Use this definition, along with the definition of the inner product of two functions, ⟨ψ|φ⟩ = ⎰ ψ^∗(x) φ(x) dx, (where the weight function w(x) is taken to be 1), to prove/show the following three statements (image).

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