identity function 恒等函数

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Identity Function-Definition, Graph & Examples

The identity function is a function which returns the same value, which was used as its argument. It is also called an identity relation or identity map or identity transformation. If f is a function, then identity relation for argument x is represented as f(x) = x, for all values of x. In terms of relations and functions, this function f: P → P defined by b = f (a) = a for each a ϵ P, where P is the set of real numbers. Both the domain and range of function here is P and the graph plotted will show a straight line passing through the origin.

Identity Function Definition

Let R be the set of real numbers. Thus, the real-valued function f : R → R by y = f(a) = a for all a ∈ R, is called the identity function. Here the domain and range (codomain) of function f are R. Hence, each element of set R has an image on itself. The graph is a straight line and it passes through the origin. The application of this function can be seen in the identity matrix.

Mathematically it can be expressed as;

f(a) = a ∀ a ∈ R

Where a is the element of set R.

For example, f(2) = 2 is an identity function.

In set theory, when a function is described as a particular kind of binary relation, the identity function is given by the identity relation or diagonal of A, where A is a set.