Comments by "MC116" (@angelmendez-rivera351) on "Graph the Square Root Function f(x) = sqrt(x - 5) and Find the Domain and Range" video.

  1. Let sqrt : [0, ∞) —> [0, ∞) be a bijection, such that sqrt(x)^2 = x everywhere. Let g : [5, ∞) —> [0, ∞) be such that g(x) = x – 5 everywhere. g is a bijection. Let f := sqrt°g. Since sqrt and g are bijections, f is a bijection. Therefore, dom(f) = dom(g) = [5, ∞), and range(f) = codom(f) = codom(sqrt) = [0, ∞). Since g(x) = x – 5 everywhere, f(x) = (sqrt°g)(x) = sqrt(x – 5) everywhere. Therefore, graph(f) = {{{x}, {x, sqrt(x – 5)}} in [5, ∞) cross [0, ∞) : x in [5, ∞)}.
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