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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