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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.

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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.

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2. Does every function have a domain?

Yes, every function has a domain.

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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.

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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.

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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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By taking the help of Linear Programming Calculator, you will get the exact solution quickly. You have to provide all your conditions and functions as input in the respective fields and press the calculate button to get the answer in seconds.

Linear Programming Calculator: Learn the procedure to solve the linear programming of the given constraints. Our free handy linear programming calculator tool is designed to help people who want to escape from mathematical calculations. One who is willing to know the detailed process involved in solving the Linear Programming of a function can read the further sections of this article.

How to Solve Objective functions with Linear Constraints?

Here, you can see the simple guidelines to solve the objective function with the given linear constraints. Follow these steps and compute the maximum and minimum of the functions.

• Take any objective function P and other linear constraints
• Out of all the constraints, compute the conditions which are having two variables for example x and y
• Convert the expression as bring one variable y
• By taking the slope of those constraints draw a graph
• Mark the feasible region and find out the vertices
• Substitute all the values of vertices in the objective function
• Check for which vertices, the function is minimum and maximum

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Example

Question: Find the feasible region for 2x+y=1000, 2x+3y=1500, x=0, y=0 and maximize and minimize for the objective function 50x+40y?

Answer:

Given that,

Objective function f(x,y)=50x+40y

Given constraints are

2x+y=1000, 2x+3y=1500, x=0, y=0

2x+y=1000

y=1000-2x

2x+3y=1500

3y=1500-2x

y=(1500-2x)/3

y=500-2x/3

The graph will be

The shaded area will be the feasible region in the above graph

The vertices are (0,500), (375,250), (500,0)

f(x,y)=50x+40y

Substitute the vertices in the objective function

f(0,500)=50*0+40*500=20,000

f(375,250)=50*375+40*250=28,750

f(500,0)=50*500+40*0=25,000

The minimum value is (0,500)

Maximum values are (275,250)

FAQ’s on Linear Programming

1. What is the process of linear programming?

Linear programming is the process of taking various linear inequalities relating to some situation and finding the best value obtained under those conditions.

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2. What is the linear function and examples?

Linear functions are graphs as a straight line format. The standard form of linear function is y=f(x)=a+bx. It has one dependent variable and one independent variable.

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3. What are the components of linear programming?

The three different equalities or inequalities or components of the linear programming are decision variables, objective function and constraints.

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4. How can you solve the linear programming problem?

Find out the feasible region for the constraints and decision variables. Point out the vertices, and substitute those values in the objective function to get the maximize and minimize values.

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5. How do you solve the maximum value in linear programming?

If linear programming can be optimized, an optimal value will occur at one of the vertices of the region representing the set of feasible solutions.

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