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What is a one-to-one function?
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In this question, weβre asked to recall the definition of a one-to-one function.
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These are also sometimes called injective functions.
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And thereβs many different ways of wording the definitions of these types of functions.
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One way is to say that they are functions where the elements in their domain correspond to, or map to, distinctive elements in their codomain.
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However, it can also be useful to see this written out in function notation.
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We would say that the function π is an injective or one-to-one function if the following condition holds.
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For any two elements of the domain of π, thatβs π₯ one and π₯ two, we have if π of π₯ one is equal to π of π₯ two, then we need π₯ one to be equal to π₯ two.
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And this is exactly the same as the statement given.
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If π evaluated at π₯ one is equal to π evaluated at π₯ two, then we must have that π₯ one is equal to π₯ two.
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In other words, every element of the range of this function corresponds to exactly one element of the domain of the function.
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Therefore, we were able to define a one-to-one function in this question.
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It is a function where the elements in its domain correspond to, or map to, distinctive elements in its codomain.