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# 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"****Step 4:**Click on the**"Reset"**

## 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).

- Interchange the x and y variables.
- Solve the equation in terms of y.
- 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) = 3x^{2} + 2 and verify it using the inverse function calculator.

**Solution:**

Given: Function y = f(x) = 3x^{2} + 2

To find the inverse of the function,

First interchange x and y, x = 3y^{2} + 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 = 3x^{2} + 2 is √ [(x - 2)/3]

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

- y = f(x) = 5x
^{3}+ 6 - y = f(x) =(x + 5) / (2x - 7)

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