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##### Asked by: Reinalda Egart

science space and astronomy# What does the inverse of a function represent?

Last Updated: 30th January, 2020

**function**normally tells you what y is if you know what x is. The

**inverse of a function**will tell you what x had to be to get that value of y. A

**function**f

^{-}

^{1}is the

**inverse**of f if. for every x in the domain of f, f

^{-}

^{1}[f(x)] = x, and.

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Furthermore, what does the inverse of a function mean?

An **inverse function** is a **function** that undoes the action of the another **function**. A **function** g is the **inverse of a function** f if whenever y=f(x) then x=g(y). In other words, applying f and then g is the same thing as doing nothing.

Additionally, how find the inverse of a function? **Finding the Inverse of a Function**

- First, replace f(x) with y .
- Replace every x with a y and replace every y with an x .
- Solve the equation from Step 2 for y .
- Replace y with f−1(x) f − 1 ( x ) .
- Verify your work by checking that (f∘f−1)(x)=x ( f ∘ f − 1 ) ( x ) = x and (f−1∘f)(x)=x ( f − 1 ∘ f ) ( x ) = x are both true.

Keeping this in consideration, why is it important to find the inverse of a function?

One 'physically significant' application of an **inverse function** is its ability to undo some physical process so that you can **determine** the input of said process. Let's say you have an observation y which is the output of a process defined by the **function** f(x) where x is the unknown input.

What is an inverse function give an example?

An **inverse function** is a **function** that will “undo” anything that the original **function** does. For **example**, we all have a way of tying our shoes, and how we tie our shoes could be called a **function**. The two mathematical operations that are taking place in the **function** f(x) are multiplication and subtraction.