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anonymous
 one year ago
Show that if f and g are onetoone, then f o g is oneto one
anonymous
 one year ago
Show that if f and g are onetoone, then f o g is oneto one

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0We assume that: f is 11 g is 11 Prove f o g is 11. Use definition of one to one ness

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0definition, a function h(x) is one to one if and only If h(x2) = h(x1) , then x2 = x1.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thats the contrapositive of "distinct inputs have distinct outputs'

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Proof: Assume x1,x2 are two arbitrary elements in the domain of f o g and that f(g(x2) = f(g(x1)) Since f is one to one f( g(x2) ) = f( g(x1) ) implies g(x2)=g(x1). Since g is one to one, g(x2)=g(x1) implies x2 = x1. We have shown that f(g(x2) = f(g(x1)) implies x2 = x1. QED
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