Inverse Function Calculator | How to Find the Inverse of a Function?

 

Inverse function calculator helps in computing the inverse value of any function that is given as input. To recall, an inverse function is a function which can reverse another function. It is also called an anti function. It is denoted as:

f(x) = y ⇔ f− 1(y) = x

How to Use the Inverse Function Calculator?

This calculator to find inverse function is an extremely easy online tool to use. Follow the below steps to find the inverse of any function.

  • Step 1: Enter any function in the input box i.e. across “The inverse function of” text.
  • Step 2: Click on “Submit” button at the bottom of the calculator.
  • Step 3: A separate window will open where the inverse of the given function will be computed.

Find a variety of Other free Maths Calculators that will save your time while doing complex calculations and get step-by-step solutions to all your problems in a matter of seconds.

How to Find the Inverse of a Function?

To find the inverse of any function, first, replace the function variable with the other variable and then solve for the other variable by replacing each other. An example is provided below for better understanding.

Example: Find the inverse of f(x) = y = 3x − 2

Solution:

First, replace f(x) with f(y).

Now, the equation y = 3x − 2 will become,

x = 3y − 2

Solve for y,

y = (x + 2)/3

Thus, the inverse of y = 3x − 2 is y = (x + 2)/3/

Frequently Asked Questions on Inverse Function

How do you find the inverse of a function?

To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.

What is the inverse of 6?

The inverse of 6 is ⅙. For any function “x”, the inverse will be “1/x”.

MCQ Questions for Class 10 Sanskrit with Answers Shemushi Bhag 2

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Class 10 Sanskrit MCQs Multiple Choice Questions with Answers

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MCQ Questions for Class 9 Sanskrit with Answers Shemushi Bhag 1

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Class 9 Sanskrit MCQs Multiple Choice Questions with Answers

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MCQ Questions for Class 9 Sanskrit Shemushi with Answers

  1. भारतीवसन्तगीतिः Class 9 MCQ
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MCQ Questions for Class 8 Sanskrit with Answers Ruchira Bhag 3

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Class 8 Sanskrit MCQs Multiple Choice Questions with Answers

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MCQ Questions for Class 8 Sanskrit Ruchira with Answers

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Domain and Range Calculator | Best Online Calculator

Domain and Range 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.

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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.


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.


Linear Programming Calculator | Handy tool to find Linear Programming

Linear Programming Calculator

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.


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.


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.


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.


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.


Inflection Point Calculator | Calculate Inflection Point

Inflection Point Calculator

Make use of this free handy Inflection Point Calculator to find the inflection points of a function within less time. Just enter function in the input fields shown below and hit on the calculate button which is in blue colour next to the input field to get the output inflection points of the given function in no time.

Inflection Point Calculator: Want to calculate the inflection point of a function in a simple way? Then you must try out this user friendly tool provided. It is one of the easiest ways that you ever find to compute the inflection point of a function. This page is all about Finding Inflection Point of the given function using a simple method and the interactive tutorial explaining each step of the process.

Steps to Find Inflection Point

Follow the below provided step by step process to get the inflection point of the function easily.

  • Take any function f(x).
  • Compute the first derivative of function f(x) with respect to x i.e f'(x).
  • Perform the second derivative of f(x) i.e f”(x) and also solve the third derivative of the function.
  • f”'(x) should not be equal to zero.
  • Make f”(x) equal to zero and find the value of variable.
  • Substitute x value in the third derivative of function to know the minimum and maximum values.
  • Replace the x value in the given function to get the y coordinate value.
  • Then, inflection points will be (x value, obtained value from function).

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Example

Question: Find the inflection points for the function f(x) = -x4 + 6x2?

Solution:

Given function is f(x) = -x4 + 6x2

f'(x) = -4x3 + 12x

f”(x) = -12x2 + 12

f”'(x) = -24x

f”(x) = 0

-12x2 + 12 = 0

12 = 12x2

Divide by 12 on both sides.

1 = x2

x = ± 1

x1 = 1, x2 = -1

Substitute x = ± 1 in f”'(x)

f”'(1) = -24(1) = -24 < 0, then it is left hand bit to right hand bi.

f”'(-1) = -24(-1) = 24 > 0, then it is left hand bit to right hand bit.

Replace x = ± in f(x)

f(1) = -1+6 = 5

f(-1) = -1 +6 = 5

Therefore, inflection points are P1(, 5), P2(-, 5)

FAQs on Inflection Point Calculator

1. How do you find inflection points on a calculator?

Provide your input function in the calculator and tap on the calculate button to get the inflection points for that function.


2. What does inflection point mean?

Inflection point is defined as the point on the curve at which the concavity of the function changes. It can be a stationary point but not local maxima or local minima.


3. Find the point of inflection for the function f(x) = x5 – 5x4?

Given that

f(x) = x5 – 5x4

f'(x) = 5x4 – 20x3

f”(x) = 20x3 – 60x2

f”'(x) = 60x2 – 120x

Neccessary inflection point condition is f”(x) = 0

20x3 – 60x2 = 0

20x2(x-3) = 0

x1 = 0, x2 = 3

Substitute x2 = 3 in the f(x)

f(3) = 35 – 5*34 = 243 – 405 = -162

Inflection Point is (3, -162).


4. What is the difference between inflection point and critical point?

A critical point is a point on the graph where the function’s rate of change is altered wither from increasing to decreasing or in some unpredictable fashion. Inflection point is a point on the function where the sign of second derivative changes (where concavity changes). A critical point becomes the inflection point if the function changes concavity at that point.


Function Calculator | Online Calculator to solve Functions

Want any assistance in solving the given function? Then, make use of this Function Calculator. This is best option for you as it gives accurate answers in fraction of seconds. Simply provide your input as the function and press on the calculate button of the calculator to avail the output in no time.

Function Calculator: This best handy calculator generates the output as x-intercept, y-intercept, slope, curvature, derivative of the function. Students can get the step by step procedure on how to solve the functions in the following sections. Have a look at them and follow whenever required. You can obtain the result along with the detailed work so that you can learn and understand the concept.

Steps by Step Procedure to Solve Functions

Here is the simple method to solve the functions. Go through these steps and understand them to compute the function easily. Using these steps, you can find the slope, x-intercept, y-intercept, and derivative values of a function effortlessly.

  • Take any function
  • To compute the x intercept set y = 0 and solve the function
  • Set x = 0 to get the y intercept value.
  • To get the slope value convert the function into this form y = mx + c
  • Where m is the slope and c is the constant, the coefficient of y should be 1.
  • The derivative of a function can be computed by applying the derivative function and getting the value.

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Example

Question: Find the x-intercept, y-intercept, slope, derivative and curvature of the function f(x) = 3x – 10?

Solution:

Given Function is

f(x) = 3x – 10 = y

Set y = 0,

0 = 3x – 10

3x = 10

x = 10/3

(10/3, 0) is x-intercept.

Set x = 0,

y = 3(0) – 10

y = -10

(0, -10) is y-intercept.

Slope:

Convert the given function into y = mx + c form

y = 3x – 10

m = 3, c = -10

Slope is 3.

Curvature is 0.

Derivative of the function is

dy/dx = d/dx(3x – 10)

= d/dx(3x) – d/dx(10)

=3

x intercept is 10/3, y intercept is -10, slope is 3, curvature is 0, derivative is 3.

Frequently Asked Questions on Function Calculator

1. What are the functions?

Functions are defined as the equation where it gives one output for every input. Function is a mathematical rule that defines the relationship between dependent and independent variables.


2. How can you represent functions?

The standard form to represent the functions are f (x) = y.

Where, x is the input

y is the output of the desired function’F represents the function.


3. What is the difference between relation and function?

Relation means collection of inputs and outputs which are related to each other in some way. If each input of the relation having exactly one output, then that relation is called a function.


4. What is the domain and co domain of a function?

Domain of a function is the set of inputs for which the function is defined. A co domain is the set of possible output values of the function.


5. What are the different types of functions?

The different types of functions are Linear function, Quadratic function, Exponential function, Power function, Polynomial function, Logarithmic function, and so on.