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Inverse Function Calculator

Enter the function f(x) into the calculator, and it will determine its inverse function x = f(y) along with detailed calculation steps.

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Inverse Function Calculator

The Inverse Function Calculator helps you find the inverse of any given function quickly and accurately. Enter the function, and the calculator reverses it while showing a clear, step-by-step solution to help you understand the process.

How to Use the Inverse Function Calculator

The calculator computes the inverse of the entered function by following these steps:

Input:

Enter a function f(x) in the input field
Click the Calculate button

Output:

The correct inverse of the given function
Step-by-step solution for better understanding

How to Find Inverse Functions Manually

To find inverse function (f^-1) manually:

Write the function using y instead of x
Swap the variables x and y
Rearrange the equation to solve for y
The resulting expression is the inverse function

An online inverse function calculator performs all these steps automatically, saving time and reducing errors.

Example:

Find the inverse of the function:

f(y) = (y + 11) / (13y + 19)

Solution:

Step 1: Swap the variables x and y

x = (y + 11) / (13y + 19)

Step 2: Multiply both sides by the denominator

x (13y + 19) = y + 11

Step 3: Expand and rearrange

13xy + 19x = y + 11

13xy - y = 11 - 19x

y (13x - 1) = 11 - 19x

Step 4: Solve for y

y = (11 - 19x) / (13x - 1)

Thus, the inverse function of (y + 11) / (13y + 19) is (11 - 19x) / (13x - 1). You can verify this result using an online inverse function finder with steps.

Reference:

For more information on inverse functions, including composition, notation, self-inverses, graphs, and derivatives, see Wikipedia: Inverse Function

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