Which Equation Is The Inverse Of Y = 100X<Sup>2</Sup>?

Introduction

As we all know, mathematics is an essential subject that plays a vital role in our daily lives. It is a universal language that helps us solve problems and understand the world around us. One of the most crucial concepts in mathematics is the inverse of a function. In this article, we will explore the inverse of the function y = 100x² and understand how to find it.

What is an Inverse Function?

An inverse function is a function that reverses the operation of another function. In other words, if we have a function f(x), its inverse function is denoted as f^-1(x) and can be defined as follows: If f(a) = b, then f^-1(b) = a For a function to have an inverse, it must be one-to-one, which means that each input has a unique output.

How to Find the Inverse of y = 100x²?

To find the inverse of y = 100x², we need to follow these steps: Step 1: Replace y with x and x with y. x = 100y² Step 2: Solve for y. y = ±sqrt(x/100) Note that we have used the ± sign because the square root of a positive number has two possible values, one positive and one negative.

Domain and Range of the Inverse Function

The domain of the inverse function is the range of the original function, which is all non-negative real numbers. The range of the inverse function is the domain of the original function, which is all non-negative real numbers.

Graphical Representation of the Inverse Function

The graph of the inverse function can be obtained by reflecting the graph of the original function about the line y = x. The graph of y = 100x² is a parabola that opens upwards, and its inverse is a curve that opens to the right.

Example Problems

Let’s solve some example problems to understand the concept better. Example 1: Find the inverse of y = 100x². Solution: Step 1: Replace y with x and x with y. x = 100y² Step 2: Solve for y. y = ±sqrt(x/100) Therefore, the inverse of y = 100x² is y = ±sqrt(x/100). Example 2: Find the domain and range of the inverse function of y = 100x². Solution: The domain of the inverse function is the range of the original function, which is all non-negative real numbers. The range of the inverse function is the domain of the original function, which is all non-negative real numbers. Therefore, the domain and range of the inverse function of y = 100x² is all non-negative real numbers.

Conclusion

In conclusion, the inverse of y = 100x² is y = ±sqrt(x/100). It is essential to understand the concept of inverse functions as it has many real-life applications, such as in engineering, physics, and finance. By following the steps mentioned above, we can find the inverse of any function.