Finding Domain of a Function

Consider functions as machines for example. If you input a value X into the function, the machine processes it and gives out another value called Y. The range of such X values that you can input into the machine or function in order to get a valid output Y is called the domain of the function. If you are ever asked to find out the domain of a function, you simply need to find out all the possible X values that will return a valid output Y.

How to find the domain of a function? Here are some tips to help address this question.

Strategy 

While learning about functions and domains, it is easy to assume that the domain of a function is real numbers only. It is easy to use your math knowledge while trying to define the domain. You can especially use algebra in order to rule out invalid numbers as part of a domain. First and foremost, you need to find and eliminate numbers that cannot be part of a domain. Fractions that cannot be defined or those that have ‘0’ in their denominator, cannot be part of a domain. This means you need to check for inputs that result in such fractions. Also, negative numbers under a square root sign need to be eliminated. 

The Domain of Variety of Functions

Generally, the method that you employ in finding the domain of a function, depends heavily on the type of function itself. Domain has to have all real numbers when you have a polynomial function without any variables in the denominator. For a graph, you simply need to check out the graph and see which values work best for X. When it comes to a relation kind of function, you need to list down X and Y coordinates. Your domain in such cases will be a list of X coordinates.

Stating the Domain Correctly

Notation for a domain can be learned easily, but when it comes to writing them down correctly, it can be tricky. It is important to write the domain correctly especially when it comes to tests or assignments. A domain has to be expressed in an open bracket then 2 endpoints of the domain that have to be separated by a comma, and lastly, a closed bracket. Depending on your location, the notation aspects could differ. Some regions tend to use the arrow sign in place of infinity signs whenever there is a requirement to express that the domain can go on infinitely.

Example of Finding Domain

Take for example, f(x) = 3/(x – 2). Any number that you input will be used in place of X on the right-side. In case a fraction is involved, and if the input results in the denominator being zero then the input has to be excluded from the domain of the fraction. If you have excelled in Math, it is easy to understand negative square roots with the help of a concept called imaginary or complex numbers.

While determining how to find the domain of a function, it is important to remember that you need to use physically possible and meaningful examples from the real world. It is also important to remember that these have to be mathematically permitted in order to be included in the domain. 

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