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

Introduction

When it comes to mathematics, one of the most important concepts is that of an inverse function. The inverse function is simply a function that undoes the effect of another function. In other words, if we apply a function f to a number x, and then apply its inverse function f^-1 to the result, we get back the original number x. In this article, we will discuss the inverse of the function y = 100x² and how to find it.

The Function y = 100x²

Before we talk about the inverse of the function y = 100x², let’s first understand what this function represents. The function y = 100x² is a quadratic function, which means it is a function of the form f(x) = ax² + bx + c, where a, b, and c are constants. In this case, a = 100, b = 0, and c = 0, which means that the function only depends on the value of x and is symmetric around the y-axis.

Finding the Inverse Function

To find the inverse of the function y = 100x², we need to solve for x in terms of y. We start by writing the equation in the form x = f^-1(y) and then solving for x. In this case, we have: y = 100x² Dividing both sides by 100, we get: y/100 = x² Taking the square root of both sides, we get: x = ±√(y/100) Notice that we get two possible values of x, one positive and one negative. This is because the function y = 100x² is not one-to-one, which means that multiple values of x can produce the same value of y.

The Domain and Range of the Inverse Function

Now that we have found the inverse of the function y = 100x², let’s discuss its domain and range. The domain of the function f(x) = 100x² is all real numbers, which means that any value of x can be plugged into the function. However, the range of the function is y ≥ 0, which means that the function only produces non-negative values of y. On the other hand, the domain of the inverse function f^-1(y) = ±√(y/100) is y ≥ 0, which means that only non-negative values of y can be plugged into the function. The range of the inverse function is all real numbers, which means that any value of x can be produced by the function.

Graphical Representation

To better understand the inverse of the function y = 100x², let’s take a look at its graph. The graph of the function is a parabola that opens upwards and passes through the origin. The graph of the inverse function is the reflection of this parabola about the line y = x, which means that the inverse function is also a parabola that opens sideways and passes through the origin.

Applications of the Inverse Function

The inverse of the function y = 100x² has many applications in mathematics and science. For example, it can be used to solve problems involving projectile motion, where the height of an object is a function of time. The inverse function can also be used to find the roots of a quadratic equation, which is a useful tool in algebra and calculus.

Conclusion

In conclusion, the inverse of the function y = 100x² is f^-1(y) = ±√(y/100), where y ≥ 0. The inverse function is a parabola that opens sideways and passes through the origin. It has many applications in mathematics and science, and is a fundamental concept in the study of functions.