A function is a rule which assigns exactly one output f(x) to every input x.
It is a bijective function.
You how to remember input and output is like a machine do the rest.
The relationship between the input and output values is typically defined by a function. In this case, if the input is 6 and the output is 4, the function could be represented as f(x) = x - 2. This function subtracts 2 from the input value to get the output value.
The imput or x value
Assuming by in you mean input and out you mean output. Input is the value that goes in while the output is the value you receive. Between these terms is a rule, called the nth term that will always work to help you find the input/output. For example. Our input is 2, and our output is 10 the rule here could be the input multiplied by 5 equals the output, or it can be something extremely difficult and unfathomable even to a banker...
It assigns exactly one output value for each input value.
It is a bijective function.
The relationship that assigns exactly one output for each input value is called a "function." In mathematical terms, for a relation to be classified as a function, every input from the domain must correspond to exactly one output in the codomain. This ensures that there are no ambiguities regarding the output for any given input. Functions are often represented as f(x), where x is the input.
The relationship where each input value results in exactly one output value is known as a function. In mathematical terms, a function assigns a unique output to each member of its domain, ensuring that no input corresponds to more than one output. This characteristic distinguishes functions from other types of relations, where an input could potentially map to multiple outputs.
It is a injective relationship. However, it need not be surjective and so will not be bijective. It will, therefore, not define an invertible function.
I found two answers for this question. A function is a rule that assigns to each value of one variable (called the independent variable) exactly one value of another variable (called the dependent variable.) A function is a rule that assigns to each input value a unique output value.
Answer - True, answer on apex.
Function
A one-to-one or injective function.
No, a function cannot have multiple values of ( y ) for one value of ( x ). By definition, a function assigns exactly one output (or value of ( y )) for each input (or value of ( x )). If a relation has multiple ( y ) values for a single ( x ), it is not classified as a 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.
A relation is not a function if it assigns the same input value to multiple output values. In other words, for a relation to be a function, each input must have exactly one output. If an input corresponds to two or more different outputs, the relation fails the vertical line test, indicating that it is not a function. For example, the relation {(1, 2), (1, 3)} is not a function because the input '1' is linked to both '2' and '3'.