In mathematics, the inverse of a function is the solution of an equation in terms of the unknown variable. Finding the inverse of a given equation means finding an equation with the same solution, but with the variables reversed. An example of this is the equation y = 5×2 + 10. If you want to find the inverse of this equation, you can simplify it to find the inverse.

How to Simplify the Equation

The first step in simplifying this equation is to interchange the variables. The equation becomes x = 5y2 + 10. This equation is then solved for y. The result is y = √(x/5 – 2). This is the equation for the inverse of y = 5×2 + 10.

Examples

To illustrate this concept further, let’s look at a few examples. For the equation y = 5×2 + 10, the inverse would be y = √(x/5 – 2). If x = 20, then the inverse of the equation is y = √(20/5 – 2) or y = 3. Now let’s look at another example. For the equation y = 3x + 1, the inverse would be x = (3y – 1)/3. If y = 6, then the inverse of the equation is x = (3(6) – 1)/3 or x = 5.

Conclusion

The inverse of an equation is the equation with the variables transposed. To find the inverse of a given equation, such as y = 5×2 + 10, you must simplify the equation to find the inverse. This can be done by interchanging the variables and then solving the equation for y. Examples of this process have been given here and should help you understand how to simplify an equation to find its inverse.