A one-to-one function, a.k.a. an injective function.
function
A function is a rule which assigns exactly one output f(x) to every input x.
A relation is any set of ordered pairs.A function is a relation in which each first element corresponds to exactly one second element
It is an invertible function.
Anything you like - it depends on the function that relates the output to the input.
It's a type of function
No, not every relation is a function. In order for a relation to be a function, each input value must map to exactly one output value. If any input value maps to multiple output values, the relation is not a function.
That's a proper function, a conformal mapping, etc.
function
Is called "function".
A one-to-one or injective function.
This is true. Furthermore, functions can be broken down into one-to-one (each input provides a different output), and onto (all of Y is used when f(x) = y).
An example of a relation that is not a function is the relation defined by the set of points {(1, 2), (1, 3), (2, 4), (3, 5)}. In this relation, the input value 1 corresponds to two different output values (2 and 3), violating the definition of a function, which states that each input must have exactly one output. Therefore, since one input maps to multiple outputs, this relation is not a function.
function
A relation has pairs of numbers. A function is a special relation where for each input there is one and only one output.
A function is a rule which assigns exactly one output f(x) to every input x.
A Function