How to find the domain of a function

The domain of the function can be defined as set of numbers which can be inserted into the given function. It can also be understood as the set of some x-values which can be put in any formal equation. On the other side, the set of the Y-values are called the range of the equation. Both of these sets are equally important to solve the equation. Take for example, the following equation:

Y= f(x),

Here X is the function of the equation. Any value attached with Y set would be called Range of the equation. The domain of any equation is the set of the input values for which the equation has produced an output. Actually, the major function of the domain is to find the value of the Y. so, in one equation, finding the domain will give you both domain and range of the function. But finding out the domain of the function is different for different equations.

Domain for different set of equations

It depends on the type of equations. Some of the basic things about finding the domain of such equations are:

• A Polynomial Function which has Radicals or Variables in the denominator – For all of this type of equations, the domain is always all the real numbers. This information makes it easy and understandable.
• Function with a Fraction with a variable in the Denominator- for such equations, you will be required to set the bottom or denominator equal to zero and then find the value of the X. that would be the domain .
• Functions containing a variable inside the radical sign –for such equation, you will be required to set the terms inside the radical sign equal to >0 and the solve the equation to the find the values of X.
• Functions containing the Natural Log (In) – for this type of equation, you would require to set the terms to > 0 and then solve the function to get its domain.
• Functions made up of Graph – Here normal checking out of the equation can work. You will be required to look into the graph to find out the values which match that of X.
• Functions containing a relation – these kinds of equations release a list of values for X and Y coordinates. Here, the list of values for X coordinates will be the domain of the function.

Writing the domain for equations

Most of the students generally take out the correct form of domain for any function. But they make mistakes while writing the answer for the domain. It is highly important to write the domain to get the correct function. Let us learn the correct format here.

The domain of the function is often expressed in an open bracket also known as Parenthesis which is then followed by two endpoints. The domain is separated by a comma followed by a closed bracket or parenthesis. The domain can be written in the following format [-1 , 5) or [5, 10]. This would mean that the domain would be inside the range of -1 to 5 in first case and 5 to 10 in the second case. Then, using the correct bracket is very important to find the domain of the function. Here is the list

• [ and ], means that the a number is included in the domain. Example, [5,10] – here both 5 and 10 are included as domain.
• ( and ), means that a number is not included in the domain. Example, (5, 10) – here both 5 and 10 are not included in the domain.
• [ and ), means one number is included and other one is excluded. Example, [5, 10) – 5 is included and 10 is excluded.
• Use of U (Union) – it is used to connect a discontinuity in the domain of a function. For example, [-1, 5) U (5, 10] means that except for the value of 5, the domain range is -1 to 10.
• Infinity and negative signs are also used to express the infinity of the domain of the function which goes to infinity.
• For infinity function, we always use [ ] and ( ).

So, as much it is important to find the right domain of a function, it is always important to write the expression clearly to get the correct answer. For most of the times, we tend to ignore this part of writing the domain but is the central concept of writing the domain. It is here that most students find wrong answers.