Injectivity & Surjectivity

Injectivity and surjectivity describe properties of a function. An injection, or one-to-one function, is a function for which no two distinct inputs produce the same output. A surjection, or onto function, is a function for which every element in the codomain has at least one corresponding input in the domain which produces that output. A function that is both injective and surjective is called bijective. Wolfram|Alpha can determine whether a given function is injective and/or surjective over a specified domain.

Injectivity

Test if a function is an injection.

Determine whether a given function is injective:

Determine injectivity on a specified domain:

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Surjectivity

Check if a function is a surjection.

Determine whether a given function is surjective:

Determine surjectivity on a specified domain:

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Bijectivity

Find out if a function is a bijection.

Determine whether a given function is bijective:

Determine bijectivity on a specified domain:

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