Domain and Range of a Function
What is a Function?
Domain and Range of a Function Suppose that you went to the vending machine in an airport. For every item such as snacks, beverages, cold drinks, and so on that you get after inserting the respective amount of coin in the machine. So, what are these machines, items, and cash all about?
Please note that each item in the machine has its respective code. Sometimes, it happens that you forgot to enter the correct product code enlisted against each item
Well, the vending machine is a function, and the domain is the “Product code” that you enter against each item provided in the machine. However, the range is the possible item you obtain after entering the product code and the coin. Therefore, domain and range are the important angles of a function. We will understand the concept of a function, range, and domain along with illustrating examples.
The Domain and the Range of a Function Example
Assume that you go to a party and gift a bouquet of Rose flowers to your friend and when your friend attends your birthday party, he gives you two bouquets of flowers. Here, if I wish to represent this scenario, we get the following relationship:
You gave ‘x’ bouquet of flowers and get ‘ bouquet of flowers, so:
Here, we have discussed a single bouquet of flowers as an input, which is a domain and if you substitute some more values, you get the following set of values, which is range:
f (x)  
2  4 
3  9 
4  16 
You might notice that this relationship gives a double return on investment. However, this is not always the case, here, if you use it, we may find the value reducing each time there is an increase in the denominator value.
Understanding Function in Simple Words
Assume that the vending machine in the Delhi Airport can accept only Rs. 10 and Rs. 50 notes to buy something.
Suppose a lady uses Rs. 20 Notes, do you think that the machine will give her the desired item? Well, no! Here, we see that the domain is the set of input values you give to a function like here we had Rs. 10 and Rs. 50 notes as the domain of the airport’s “Vending Machine”. Therefore, it doesn’t matter how much money that lady put in the machine, she will get her desired item, like Burger. This is the time, the concept of the range comes into play here, range is the possible outputs machine can give.
For instance, if you put 5 notes of Rs. 50 into the machine, you may get any five items that are of this amount. These items corresponding to this amount are the range of a function. Now, what is the domain and the range, and how to find them?
Now, let us solve a question to understand the concept of the domain and range a bit more.
Solved Examples on the Domain and Range of a Function
 Find the range of.
Here, we notice that on putting p = 3 (the domain value), we get an undefined output, so the range of will be R – {3}.
However, if there is a function: then the function is a square root and negative values won’t give us the desired output.
The minimum value we get here at m = 1 is 0. Maximum value can go up to infinity as we keep on increasing m. So, the range, in this case, is [0, ).

Find the Domain values for which the Functions are equal.
Firstly, let us equate both the functions:
We get
Now, let us solve this quadratic equation:
We get the values of a: ½ and – 2; these are domain values. For more information, please visit the website and get a detailed explanation of all the maths concepts. Cuemath’s website has a lot of mathematical concepts explained in a fun and interactive way.