A one-to-one function is a function in which each input value is mapped to one unique output value. In other words, no two input elements have the same output. A function f is one-to-one if no two elements in the domain of f correspond to the same element in the range of f. A function g is one-to-one if every element of the range of g corresponds to exactly one element of the domain of g. A function with domain A is called a one-to-one function if every f(x)-value in the range B comes from only one x-value in A. In mathematical terms, one-to-one functions are functions in which there are equal numbers of items in the domain and in the range, or one can only be paired with another item.
To determine if a function is one-to-one, one can use the horizontal line test. If no horizontal line intersects the graph of the function in more than one point, then the function is one-to-one. A function has an inverse if and only if the function is one-to-one.
