Question: Let g : R R satisfy the relation g(x + y) = g(x) g(y) for all x, y in R. Show that if g

Let g : R → R satisfy the relation g(x + y) = g(x) g(y) for all x, y in R. Show that if g is continuous at x = 0, then g is continuous at every point of R. Also if we have g(a) = 0 for some a ∈ R, then g(x) = 0 for all x ∈ R.

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