One-to-One Function

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One-to-One Function

In mathematics, a function is a rule that assigns to each element in a set (called the domain) exactly one element in another set (called the range). A function is said to be a one-to-one function, or a bijective function if every element in the range corresponds to exactly one element in the domain.

One-to-one functions have several important properties:

  • They have an inverse function, a function that "undoes" the original function. For instance, if f(x) = 2x is a one-to-one function, its inverse function is f^(-1)(x) = x / 2, which undoes the original function by dividing x by 2.
  • They are invertible, which means that their inverse function exists and is itself a function.
  • They maintain uniqueness, which means that if two elements in the domain are different, their images in the range too will be different.

One-to-one functions are helpful in many views, including in cryptography (to encode and decode messages), computer science (to describe unique keys in databases), and other scopes of mathematics.

Samples of one-to-one functions contain the function f(x) = x^2, which maps each element in the domain to its square in the range, and the function f(x) = x + 3, which adds 3 to each element in the domain.

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