anonymous
  • anonymous
Show that if f and g are one-to-one, then f o g is one-to one
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
We assume that: f is 1-1 g is 1-1 Prove f o g is 1-1. Use definition of one to one ness
anonymous
  • anonymous
definition, a function h(x) is one to one if and only If h(x2) = h(x1) , then x2 = x1.
anonymous
  • anonymous
thats the contrapositive of "distinct inputs have distinct outputs'

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anonymous
  • anonymous
Proof: 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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