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# Inverse Function Calculator

To use inverse function calculator, enter the function and hit the **calculate** button

## Inverse Function Calculator

Inverse function calculator is used to calculate the inverse of the given function. This inverse of a function calculator provides the step-by-step solution to the given function.

## What is an Inverse Function?

A function that `"undo"`

the result of another function is called an **inverse function**. In other words, if **g** is a function that "**reverses**" the impact of **g**, mapping each element of set **X** to a distinct element of set **Y**, then h is said to be the inverse function of **g**.

Let **g: A → B** be a function more formally. **H** is the inverse function of **g** if there is a function h: B A such that `h(g(x)) = x`

for all** x** in** A **and `g(h(y)) = y`

for all **y** in **B**. Applying **f** and then **g** (or **g **and then **f**) produces the identity function.

## How can we find the inverse of a function?

To find the inverse of a function we have to follow some steps.

- Put the given function equal to
**y**. - Separate the domain variable for the function.
- In the last change the name of the variable involved in the inverse.

## Pictorial Representation:

Let two sets **A** and **B**. One set contains elements `{x, y,z}`

, and the other is `{1,2,3}`

. **A** to **B** is a function, meaning every element of **A** has a unique image in set **B**. For inverse, the given function must be a `one-to-one function`

.

A one-to-one function means all element has a unique and separate image in the **2 ^{nd}** set.

**g**is the function then the inverse is

**g**.

^{-1}Pathway to find the inverse function

For the purpose to get the solution, we have to understand this with the help of a numerical example.

**Example:**

Find the inverse of the function `g(x) = 2x + 18`

.

**Solution:**

**Step 1:** First we have replaced **g(x)** with y from the definition of the function **y = g(x)**

y = 2x + 18

**Step 2:** Now separate the variable **x**.

y – 18 = 2x

x = (y - 18) / 2

**Step 3: g(x) = y** then **x = g-1(y) **

g^{-1}(y) = (y - 18) / 2

**Step 4: **Now change the name of the variable from **y** to **x**. because the function is independent of the variable name.

g^{-1}(x) = (x - 18) / 2