inverse functions definition with examples
Tags: education, mathematics, inverse, functions
Published: 2022-09-21 18:56:05


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In this post, we'll look at what an inverse function is and how it can help us solve problems in math. We'll also go over some examples to show you how they work.

## Definition of the inverse function

[Inverse functions](https://www.turito.com/learn/math/inverse-functions) have the same form but opposite behavior. If a function is, then its inverse—also known as its reciprocal—is. In other words, if you multiply by to get, then and are inverse functions

Example 1

The inverse of a function is its opposite. It has the same inputs as the original function, but it produces the opposite output. For example, if you have an equation y = f(x) and you want to find its inverse, then you need to rearrange it so that x is equal to some form of y: y = f(-x).

For example, let's say we want to find the inverse function for f(x) = 5x + 4. To do this, use your knowledge of algebraic operations on functions to get rid of all terms other than x and then set up an equation where x equals some form of y: 5x + 4 = 9y; therefore y = -5/9. This means that if we input a number into our original function (5x + 4), we'll get back its reciprocal (-5/9).

Example 2

Let's look at a second example.

In this case, the function is the inverse of the function below:

The graph of this [inverse function](https://www.turito.com/learn/math/inverse-functions) is illustrated below. As you can see, not only does it not pass through (0,1), but it also has an x-intercept of -1 and a y-intercept of 1.

Example 3

In this example, you will learn how to identify an inverse function.

Suppose that we have a parent function \(f(x)\), and it has a graph that looks like this:

The graph of the [inverse function](https://www.turito.com/learn/math/inverse-functions) is the same as the graph of its parent function but reflected over the vertical axis (also called “flipped”). In other words, instead of it being drawn above or below the axis, it will be swept up or down.

understanding inverse functions and their properties can help you do better in math

Understanding inverse functions and their properties can help you do better in math. Inverse functions are a tool that can help you solve problems, and understanding how to use them will improve your skills in problem-solving, as well as other areas of math.

Inverse Functions

The first step to understanding [inverse functions](https://www.turito.com/learn/math/inverse-functions) is knowing what they are: an inverse function is a relationship between two numbers or expressions that have been reversed. For example, the function f(x) = x2 has an inverse relationship with g(x) = x2; if you apply the first function to any number x and get output y, applying the second function will give you back x when given y as input. If we want to find out what y would be if we were given 2 as input (and thus were using g(2)), then we could take 2*f(2).

Conclusion

In this article, we have discussed the definition of [inverse functions](https://www.turito.com/learn/math/inverse-functions) and examples of inverse functions with step-by-step video explanations. We hope that you find it useful in your studies!