Flashcards
IFTfCF defs
Cards in this deck (7)
- 1InjectiveA real function f:X->Y is injective if f(x1)≠f(x2) whenever x1 and x2 in X and x1≠x2.
Or, f is injective, if for each y in Y there exists at most one x in X such that f(x)=y - 2SurjectiveThe function f is surjective if, for each y in Y, there exists at least one x in X such that f(x)=y
- 3BijectiveThe function f is bijective if it is both injective and surjective
- 4Inverse functionLet f:X->Y be a function. The inverse function f^(-1);Y->X is defined by f^(-1)(y)=x for each y in Y, where x is the unique element of X such that f(x)=y
- 5Strictly increasingA real function f:X->Y is strictly increasing if f(x1)
- 6Strictly decreasingA real function f:X->Y is strictly decreasing if f(x1)>f(x2) whenever x1,x2 in X and x1
- 7Strictly monotoneA real function f:X->Y is strictly monotone if it is either strictly increasing or strictly decreasing
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- Description
- Definitions for 'Inverse function theorem for continuous functions'
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- Chelsea Hilditch
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