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What is a Domain and Range in Mathematics?


The Functions in the study of Mathematics is quite an interesting subject. It says when we input a set of numbers we usually get a set of new different types of numbers. This means the input combines to form a totally new output. In Maths, we say that the domain is the inputs while the range is the output or the result that we get from the input. In this content, we will know more about domain and range.

Domain and Range – Sets of X and Y Coordinates

The domain and range in the mathematical sets are the relations which are these sets of all the X-coordinates and the Y-coordinates. These coordinates normally work in pairs and that too respectively. For example: If we choose R to be the relation, then  R = {(1, 2), (2, 2), (3, 3), (4, 3)} here we say that the domain is the set of all the X-coordinates which is {1, 2, 3, 4}, and the range is the set of all the Y-coordinates {2, 3}

What Will Be The Domain of a Function?

The Domain of the function is the values of the function which fit right into it. The domain of the function is a whole set of all the possible inputs which is present in the functions. Suppose a function – f(x) = 6x, here all the values of x are to be inputted. Thus, the domain is nothing but the set of all the natural numbers and the range is the output that we have.  In general, it might define the real numbers hence the domain is the set of all the real numbers that is being denoted by  (-∞, ∞). The general formulae which are required to find the domain are the different types of functions. We suppose, the R is the set of all the real numbers.

  • The domain of any polynomial equation is the linear, quadratic, cubic function is represented by R.
  • The domain which is the square root function will be √x is x≥0.
  • A domain that is of an exponential function is the form of R.
  • x>0 is the domain of the log function.
  • In order to find the domain of the rational function y = f(x), the set of the denominator will not be equal to 0.

What Will Be the Range of a Function?

The range of all the functions will be the set of all its output. Here we will consider the set of the function, where f(x) = 2x and each of the P and Q are the set of all the natural numbers.

In this we can say that P is the domain while Q is the co-domain here. The output of this function is the range here.  The general formulae of Range are as follows:

  • R is the range of the linear equation.
  • The range of the quadratic function y = a(x-h)2 + k is:
    y≥k, if a>0 and
    y≤k, if a<0
  • The range of the square root function is y≥0.
  • The range of the exponential function of y is y>0.
  • R is also the range of log functions.

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This content was about the domain and range, the students by now are clear on this topic, and have gained the required insight for the same. Further, the students can also explore the in-depth study of the same concept or illustrate more on other related mathematical concepts. Visit Cuemath and explore your maths zeal.