Domain and Range Calculator | Best Online Calculator

Use this handy Domain and Range Calculator to get the exact answer for your function instantly. All you need to do is enter the function in the input box and press the calculate button which is in blue colour to display the domain and range values of that particular function in seconds.

Domain and Range Calculator: Struggling to find the domain and range of any function. Then you can avail the handy tool Domain and Range Calculator to get the output instantaneously. In the below section, you can check the steps to solve the domain and range for square root function and polynomial function, and others. For your better understanding, we are also giving the example questions.

Steps to get the Domain and Range for Square Root or other Functions

You can observe the simple steps through which we can know the domain and range of any real valued function. Use these steps, when you are searching for a detailed process to solve the domain & range.

  • Take any real valued function
  • Find any real number for x get a meaningful output
  • Domain is all the real numbers, except for which number we are not getting the meaningful output.
  • Do the inverse function by interchanging the x and y values
  • Again, get the real numbers for which we are getting a meaningful output
  • Range is also all the real numbers except those set of numbers for which you are not getting the output.

How to Find the Domain & Range for Real Valued Function?

  • Take any real valued linear function
  • We know that real functions are the lines that continue forever in each direction
  • Check that by substituting the any real number in the function, gives an output or not
  • Then all the real numbers are domain and range

Example

 

Question1: Find the domain and range of the function y=x2-3x-4/x+1

 

Solution

Given function is y=x2-3x-4/x+1

We can say that the function is not defined at x=-1

Because when we substitute -1for x, we get zero in the denominator

So, the domain is all real numbers except -1

Find the factors of numerator

y=(x+1)(x-4)/(x+1)

y=x-4

Substitute the x=-1 in the above equation

y=-1-4

y=-5

This means, the function is not defined when y=-5 and x=-1

Therefore the range of the function is {y belongs to R | y=!-5} and domain is {y belongs to R | x=!-1}

Question2:
What are the domain and range of the function f(x)=-2+sqrt(x+5)?

 

Answer:

Given function f(x)=-2+sqrt(x+5)

This is a radical function

Square root must be always positive or zero

sqrt(x+5)>=0, then -2+sqrt(x+5)>=-2

range is all real numbers such that f(x)>=-2

The domain of the radical equation is any x value for which the sign is not negative.

That means, x+5>=0

x>=-5

FAQs on Domain and Range

1. What is the domain and range?

Domain is a set of all values for which the function is mathematically defined. The range is the set of all possible output values (commonly the variable y or f(x)), which result from using a particular function.


2. Does every function have a domain?

Yes, every function has a domain.


3. What is the difference between domain and range?

Domain is all the values that go into function and range is all values that come out.


4. How do you write domain and range?

Domain and range are always written from smaller to larger values or from left to right for domain and from bottom to the top of the graph for range.


5. How do you find the domain and range on a calculator?

Enter input in the specified box and click on the calculate button to display output.


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