## Introduction

Understanding inverse equations can be tricky, but it is an essential part of mathematics. In this article, we will discuss the inverse of the equation y = 100x^{2}. We’ll explore what inverse equations are, why they matter, and how to find them.

## What are Inverse Equations?

Inverse equations are two equations that are related to each other in such a way that when one equation is solved for a variable, the other equation is obtained. In simpler terms, if we have an equation f(x) = y, then the inverse of this equation is g(y) = x.

## Why do Inverse Equations Matter?

Inverse equations are essential in many areas of mathematics, including calculus, algebra, and geometry. They allow us to solve problems that would be impossible to solve otherwise. For instance, in calculus, the inverse of a derivative is an integral, which helps us find the area under a curve.

## Finding the Inverse of y = 100x^{2}

To find the inverse of y = 100x^{2}, we need to solve for x. We start by replacing y with x and then solving for x.

x = 100y^{1/2}

We can simplify this equation by dividing both sides by 100.

x/100 = y^{1/2}

Now, we need to isolate y on one side of the equation. To do this, we square both sides of the equation.

(x/100)^{2} = y

Therefore, the inverse of y = 100x^{2} is x = (y/100)^{1/2}.

## Verifying the Inverse

To verify that x = (y/100)^{1/2} is indeed the inverse of y = 100x^{2}, we need to check if the composition of the two functions gives us the identity function. The identity function is a function that returns the same value that was inputted into it.

To find the composition of the two functions, we substitute y = 100x^{2} into x = (y/100)^{1/2}.

x = ((100x^{2})/100)^{1/2}

x = x

Therefore, the composition of the two functions gives us the identity function, which means that x = (y/100)^{1/2} is indeed the inverse of y = 100x^{2}.

## Conclusion

In conclusion, the inverse of y = 100x^{2} is x = (y/100)^{1/2}. Inverse equations are essential in mathematics and allow us to solve problems that would be impossible to solve otherwise. It’s essential to understand the concept of inverse equations and how to find them to become a proficient mathematician.