Algebra Examples

Determine if Bijective (One-to-One)
,
Since for each value of there is one and only one value of , the given relation is a function.
The relation is a function.
Since the relation is a function and for each value of there is one and only one value of , the given relation is a one-to-one function.
The relation is a one-to-one function.
Every point in the range is the value of for at least one point in the domain, so this is a surjective function.
Surjective function
Since is injective (one to one) and surjective, then it is bijective function.
Bijective function
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