What is a one to one function?

A one-to-one function, also known as an injective function, is a function where each element of the range (output) corresponds to a unique element of the domain (input). In simpler terms, no two different elements in the domain map to the same element in the range.

Here's a breakdown of key aspects:

• Definition: A function f is one-to-one if for any a and b in the domain of f, if f(a) = f(b), then a = b. This can also be expressed as: if a ≠ b, then f(a) ≠ f(b). For more information: https://www.wikiwhat.page/kavramlar/Definition%20of%20One-to-One%20Function

• Horizontal Line Test: A graphical test to determine if a function is one-to-one. If any horizontal line intersects the graph of the function at more than one point, the function is not one-to-one. For more information: https://www.wikiwhat.page/kavramlar/Horizontal%20Line%20Test

• Inverse Function: A one-to-one function has an https://www.wikiwhat.page/kavramlar/Inverse%20Function. Only one-to-one functions are invertible. The inverse function "undoes" the original function.

• Examples:

  • f(x) = x + 5 is one-to-one.
  • f(x) = x² is not one-to-one (e.g., f(2) = 4 and f(-2) = 4).

• Importance: One-to-one functions are important in various areas of mathematics, including calculus, linear algebra, and cryptography. Their invertibility is a crucial property.