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highmath
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Why multi-valued function is a function?
A multi-value function is a mathematical concept that assigns more than one output value to a single input value. This is in contrast to a traditional function, which only has one output value for every input value.
Multi-value functions are used to model real-world situations where a single input can have multiple outcomes. They are also useful in solving certain mathematical problems, such as finding the roots of equations.
Examples of multi-value functions include the inverse trigonometric functions (arcsin, arccos, arctan), which have multiple possible output values for a given input value. Another example is the square root function, which can have both a positive and a negative output for a given input.
Multi-value functions are typically represented using a graph, with the input values on the x-axis and the output values on the y-axis. In some cases, a multi-value function may also be represented using a table of values.
A multi-value function is a type of relation, but not all relations are multi-value functions. A relation is a set of ordered pairs, while a multi-value function is a relation that follows specific rules, such as each input having multiple corresponding outputs. In other words, a multi-value function is a specific type of relation that has multiple outputs for a single input.