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Find (f g)(x) for f and g below f(x) = 3x 4 (6) g(x) = x2 1 x (7) When composing functions we always read from right to left So, rst, we will plug x into g (which is already done) and then g into f What this means, is that wherever we see an x in f we will plug in g That is, g acts as our new variable and we have f(g(x)) Then by the Fundamental Theorem of Calculus F ′ (x) = f(x) Changing variables u = x t we get g(x) = ∫b af(x t)dt = ∫b x a xf(u)du = F(b x) − F(x a) Differentiating the above we finally have g ′ (x) = F ′ (b x) − F ′ (x a) = f(b x) − f(x a) Share answered Jun 1 ' at 2225 Tony419(A u B′) ∩ B = {e, f} (g) (A u B) ∩ (A u B′) The first part is the answer to part (a), The last part is the answer to part (e) So (A u B) ∩ (A u B′) means "the set whose members are members of the answer to part (a) and members to the answer to part (e)" So

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