A function in mathematics means a binary relation between two sets. Likewise, every component of the first set is different from that of others. The term identity function refers to any mathematical theorem that maintains the value of the variable yet after executing the action it specifies. The other name of the identity function is identity relation or the identity map. Specifically, the identity of function arrives at the same value that was used as the argument. If you are a maths pro, keep reading with us to learn the domain and range of identity function in this article.

**1. What is an Identity of Function?**

The **function that yields the same result after an argument is used** is known as the identity function. Typically, it is represented by the F function, and the argument is displayed using X. Mathematics’ real value function is illustrated as Y when a real set of integers is represented by R. Since Y = F (X) for all X **∈** R, this function is known as an identity function because it has, in this case, returned to the same value. (See What does How Many More mean in Math?)

**2. How are the Identity of Function Mathematically represented?**

The identity of function is represented as **f(a) = a ∀ a ∈ R.**

**3. What are the Properties of Identity of Function?**

Below are the properties of identity of function you need to know:

- The identity of the function returns to the same value as the argument.
- Every positive integer can be multiplied by the identity function. Especially the number is multiplied by 1.
- It is shown in the form of an identity matrix in the case of m-dimensional vector spaces.
- In a topological space, the identity function is a continuous function.

**4. What is the Domain and Range of Identity Function?**

The domain and range are the real numbers for the identity function. You will know more about the identity function formula as you read till the end. (See How can You Find the Sum of the First 100 Natural Numbers?)

**5. Are Domain and Range of Identity Function Same?**

**Yes**, the domain and range of identity function are the same. This is due to the fact that each element in the domain maps to a single element in the co-domain. Therefore, if you pay great attention, the identity function is also R since the domain is R.

**6. Does Every Function have a Domain?**

**Yes**, every function has a domain. Read this article till the end to know more about identity function real life examples. (See What is a Mathematical Sentence Example?)

**7. What are Algebraic Identities?**

Now that your identity of function basics is clear, let us move forward. Algebraic identities are algebraic equations that are true regardless of the value of each variable. Additionally, they are employed in the factorization of polynomials. Algebraic identities are employed in this manner for the calculation of algebraic expressions and the solution of various polynomials. Some algebraic identities are:

**Identity 1**: (a + b)^{2 }= a^{2 }+ b^{2 }+ 2ab

**Identity 2**: (a − b)^{2 } = a^{2 }+ b^{2 }– 2ab

**Identity 3**: a^{2 }− b^{2 } = (a + b) (a − b)

**Identity 4**: (x + a) (x + b) = x^{2 }+ (a + b) x + ab

**8. What is an Identity Function Formula?**

The identity function formula is **f(a) = a ∀ a ∈ R. **Must see What are the Prime Numbers between 20 and 30?

**9. What is an Identity Function Real Life Example?**

Are you also wondering about identity function real life example? If so, here is one. Dropping a penny from a building’s roof and timing the distance traveled.

**10. What is a Constant Function?**

The simplest type of **real-valued function** is a constant function, which is used to define a number that doesn’t change over time. Constant functions have graphs in the plane that are horizontal lines and linear functions. A constant function is one that has a range that remains constant for all possible domain values. On a graph, a constant function is shown as a straight line that is perpendicular to the x-axis. The x-value, which is represented on the x-axis, serves as the function’s domain, and y, or f(x), which is indicated with reference to the y-axis, serves as the function’s range.

**11. What is an Identity Function Graph?**

The graph of the identity function is a **straight line that goes through zero**. As a result, the graph’s point on the straight line represents the identity function, which has an identical relationship to the values on the x and y axes. The y-axis represents the value function, and the x-axis represents the parameter. Read Which Correlation is the Strongest?

**12. What is a Modulus Function?**

Regardless of the sign, a modulus function returns the **magnitude of a number.** The absolute value function is another name for it. The modulus function, represented in mathematics by the symbol x, determines the modulus of a real number x. It provides x’s non-negative value. A number’s distance from the origin or zero is also thought of as the number’s modulus or absolute value.

A polynomial function is represented by the identity function. It is a particular kind of linear function where the result and input are identical. An identity relation or identity map is another name for the identity function. The domain and range of identity function are the real numbers. It returns to the same value with which the output was entered. Now if you are working on the identity of function then make sure you remember these things. (Also read What is Number System Aptitude?)