Let DCC be a domain. When f: DC is a function of class C(D), we define:...

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Let DCC be a domain. When f: DC is a function of class C¹(D), we define: af(x,y) = (()_91(x,y)), (* Əy f(x,y) = (f(y) + f(x,y)). (3) (i) Show that when f and g are C¹ on D we have af = af and (fg) = (af)g+ f(@g). (ii) Suppose now that f is analytic on D and that [f] is constant (that is, the mapz|f(2)| is constant on D). Use the preceding question to show that f is constant. Let DCC be a domain. When f: DC is a function of class C¹(D), we define: af(x,y) = (()_91(x,y)), (* Əy f(x,y) = (f(y) + f(x,y)). (3) (i) Show that when f and g are C¹ on D we have af = af and (fg) = (af)g+ f(@g). (ii) Suppose now that f is analytic on D and that [f] is constant (that is, the mapz|f(2)| is constant on D). Use the preceding question to show that f is constant.