Question: Please Answer in detail. 3.20 Let D : C (R) - Co (R) be defined by D(f) = df dx a. Let f(x) = ex

Please Answer in detail.

Please Answer in detail. 3.20 Let D : C (R) - Co
3.20 Let D : C (R) - Co (R) be defined by D(f) = df dx a. Let f(x) = ex and g(x) = x2. Show by direct computation that D(2f + 3g) = 2D(f) + 3D(g) b. Prove that Tis a linear transformation. c. Let U : Co() - Co (IR) be defined by U(f) = D(xf) Is U linear? If so, prove it. If not, show by an explicit example that one of the linearity properties fails

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