Question: Prove that multiplication Mh[f(x)] = h(x) f(x) by a fixed function h Cn[a, b] defines a linear operator Mh: Cn[a, b] Cn[a, b].

Prove that multiplication Mh[f(x)] = h(x) f(x) by a fixed function h ∈ Cn[a, b] defines a linear operator Mh: Cn[a, b] → Cn[a, b]. Which result from calculus do you need to complete the proof?

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