1. For I = (i1,..., in) € (NU {0})", denote and |I| = ₁ + • + in X¹ = x²¹x²2² A polynomial f : R → R is a function of the form f(x) = Σ αιχ |I|≤d where a, ER is a constant. Show that f is continuous (Hint: write f as a composition of some simple functions that are clearly continuous).

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