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# Let f(x) = 4 for x >= 0, f(x) = 0 for x < 0, and g(x) = x^2 for all x. Thus dom(f) = dom(g) = all real numbers.Determine the functions f + g, fg, f...

Let f(x) = 4 for x >= 0, f(x) = 0 for x < 0, and g(x) = x^2 for all x. Thus dom(f) = dom(g) = all real numbers.Determine the functions f + g, fg, f of g, g of f. Specify their domains and whether or not the functions are continuous.

My work: f + g = f(x) + g(x) = 4 + x^2 if x >= 0 and x^2 if x < 0, both are continuousfg = f(x) * g(x) = 4x^2 if x >= 0 and 0 if x < 0, only 4x^2 is continuous.f of g = f(g(x)) = f(x^2) = ??g of f = g(f(x)) = g(4) = 4^2 = 16 if x >= 0 or g(0) = 0^2 = 0 if x < 0, not continuous.

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