Properties of Identity Function
Some key properties of the identity function:
- The identity function is a real-valued linear function.
- The domain and range of the identity function are the same.
- The graph of the identity function is a straight line that makes a 45° angle with both the x-axis and y-axis. The slope of the graph is always 1.
- The identity function is a one-to-one and onto function.
- Composing the identity function with itself results in the identity function, i.e. g ∘ g(y) = y.
- The inverse of the identity function is the identity function itself.
Derivative of Identity Function
Derivative of identity function is 1.
As derivative is defined as the rate of change of the function with respect to other variable or independent variable.
Let Identity function f(x) = x,
Use derivative formula,
[Tex]\frac{d}{dx}(x)=1[/Tex]
The derivative of Identity function f(x) with respect to ‘x’ is,
[Tex]\frac{d}{dx}(f(x))=\frac{d}{dx}(x)=1[/Tex]
The derivative of Identity function is ‘1’.
Integral of Identity Function
Integral of identity function is x2/2 + C.
Integral of a function is to find the area under graph of a function for some interval.
Let Identity function f(x)=x,
Use Integral formula,
[Tex]\int x \ dx=\frac{x^2}{2}[/Tex]
The Integral of the Identity function f(x) is,
[Tex]\int f(x) \ dx=\int x \ dx=\frac{x^2}{2} + C[/Tex]
Where C is constant of integration.
Identity Function
An identity function is also known as an identity relation, identity map, or identity transformation. It is one of the many types of functions found in mathematics. It is a function that maps each element in a set to itself, resulting in an output that is identical to the input.
In other words, an identity function ensures that each element in the domain is mapped onto itself in the range, maintaining the equality between the pre-image and image. In this article, we will be learning about all things related to Identity Function.
Table of Content
- What Is an Identity Function?
- Domain and Range of Identity Function
- Graphical Representation of Identity Function
- Properties of Identity Function
- How to Identify an Identity Function?