3. What it means to be well-defined: (a) Let C(0, 1]) be the vector space of complex-valued continuous functions on Dirac function oo : C([0, 1]) -> C by 0, 1]. Define the do(f f(0) Prove that for all a, ßE R and f,g E C((0,1]), we have o(afBg)ado(f)+ Bo(g) C(0, 1) (In other words, 60 is a linear functional on (b) Let R(0, 1]) be the vector space of Riemann-integrable functions on transformation? Explain your answer 0, 1. Is o also a linear carefully.

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