Inverse Function Calculator

Inverse Function Calculator computes the inverse value for a given function. A function that can reverse another function is known as the inverse of that function. The inverse of a function, say f, is usually denoted as f^-1.

What is Inverse Function Calculator?

Inverse Function Calculator is an online tool that helps find the inverse of a given function. Suppose g(x) is the inverse of f(x). Then f maps an element 'a' to 'b' while g maps the element 'b' to 'a'. To use this inverse function calculator, enter the function in the input box.

Inverse Function Calculator

How to Use Inverse Function Calculator?

Please follow the steps below to find the inverse function using the online inverse function calculator:

• Step 1: Go to Cuemath’s online inverse function calculator.
• Step 2: Enter the function in the given input box of the inverse function calculator.
• Step 3: Click on the "Solve" button to find the inverse of the given function.
• Step 4: Click on the "Reset" button to clear the field and enter a new function.

How Does Inverse Function Calculator Work?

If we a have a function f such that f: A→B. Then A is known as the domain while B is the co-domain. Based on the type of mapping, functions can be classified into the following three types.

• Injective Function - If a function maps each distinct element of its domain to each individual element of its co-domain, it is known as an injective function.
• Surjective function - If a function maps one or more elements of its domain to the same element of its co-domain, it is called a surjective function.
• Bijective Function - A bijective function is one that is both a surjective and an injective function.

The inverse of a function can only exist, if it is a bijective function. The steps given below can be followed to find the inverse of a function, y = f(x).

1. Interchange the x and y variables.
2. Solve the equation in terms of y.
3. Finally, y is replaced with f^-1(x). This gives the inverse of the function.

Solved Examples on Inverse Function Calculator

Example 1:

Find the inverse of the function y = f(x) = 4x - 9 and verify it using the inverse function calculator.

Solution:

Given: Function y = f(x) = 4x - 9

To find the inverse of the function,

First interchange x and y, x = 4y - 9

And solve for y, y = (x + 9) / 4

Replace y with f ^-1(x) = (x + 9) / 4

Therefore, the inverse of the given function y = 4x - 9 is (x + 9) / 4

Example 2:

Find the inverse of the function y = f(x) = 3x² + 2 and verify it using the inverse function calculator.

Solution:

Given: Function y = f(x) = 3x² + 2

To find the inverse of the function,

First interchange x and y, x = 3y² + 2

And solve for y, y = √ [(x - 2)/3]

Replace y with f ^-1(x) = √ [(x - 2)/3]

Therefore, the inverse of the given function y = 3x² + 2 is √ [(x - 2)/3]

Now, try the inverse function calculator and find the inverse for the given functions:

• y = f(x) = 5x³ + 6
• y = f(x) =(x + 5) / (2x - 7)

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