Which Equation is the Inverse of y = 7x^2 - 10?

When dealing with mathematical equations, it is important to understand the concept of inverse equations. An inverse equation is a mathematical expression that reverses the operations of another equation. In this article, we will explore the inverse equation of a given quadratic equation, specifically y = 7x^2 - 10. By the end, you will have a clear understanding of how to find the inverse equation and the steps involved in the process.

Mathematics

Understanding Inverse Equations:

To find the inverse equation of a given equation, we need to swap the dependent and independent variables. In other words, we interchange the roles of x and y in the original equation. Let's follow this process for the equation y = 7x^2 - 10 to determine its inverse equation.

Step 1: Swap the Variables:

In the original equation, y is the dependent variable, whereas x is the independent variable. To find the inverse equation, we switch their roles. Therefore, the dependent variable becomes x, and the independent variable becomes y.

Inverse equation: x = 7y^2 - 10

Step 2: Solve for y:

Now that we have the inverse equation x = 7y^2 - 10, we need to isolate y to find its expression. Let's solve the equation for y.

x = 7y^2 - 10

Step 3: Rearrange the Equation:

To isolate y, we rearrange the equation by bringing the constant term to the other side.

x + 10 = 7y^2

Step 4: Divide by the Coefficient:

To solve for y^2, we divide both sides of the equation by the coefficient of y^2, which is 7.

(x + 10)/7 = y^2

Which equation is the inverse of y = 7x2 – 10?

Step 5: Take the Square Root:

To obtain y, we take the square root of both sides of the equation.

√[(x + 10)/7] = y

Inverse Equation: After completing the steps, we find the inverse equation of y = 7x^2 - 10 to be:

y = √[(x + 10)/7]

Comparison Table:

For a clearer understanding, let's compare the original equation and its inverse equation side by side in a table:
 

In this article, we discussed the concept of inverse equations and how to find the inverse equation of a given quadratic equation. We demonstrated the step-by-step process for finding the inverse equation of y = 7x^2 - 10 and arrived at the final result, which is y = √[(x + 10)/7]. Understanding inverse equations allows us to reverse the operations performed in a given equation and provides valuable insights in various mathematical applications.