Question: Let f(x) = ax + b and g(x) = cx2 + dx, where a, b, c, and d are constants. Compute f g and g

Let f(x) = ax + b and g(x) = cx2 + dx, where a, b, c, and d are constants. Compute f g and g f. Determine for which constants a, b, c, and d it is true that f g = g f. (Hint: Note that polynomials dnx n + dn1x n1 + + d1x + d0 and enx n + en1x n1 + + e1x + e0 are equal as functions if and only if dn = en, dn1 = en1, . . . , d1 = e1, d0 = e0.)

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