Are you struggling with creating an inverse formula? Don’t worry! In this step-by-step guide, we will walk you through the process of creating an inverse formula. So, let’s dive right in!

What is an Inverse Formula?

An inverse formula, also known as an inverse function, is a mathematical operation that undoes another operation. It helps us find the original value before the operation was performed. In simple terms, if we have a function f(x), the inverse function is represented as f-1(x).

Step 1: Understanding the Original Formula

The first step in creating an inverse formula is to understand the original formula. You need to have a clear understanding of the function for which you want to find the inverse. Let’s consider an example where the original formula is f(x) = 2x + 5.

Step 2: Swap Variables

In order to create the inverse formula, we need to swap the variables in the original formula. In our example, we need to replace f(x) with x and x with f(x). This step will help us isolate the original input value, x. After swapping, our formula will be x = 2f-1(x) + 5.

Step 3: Solve for f-1(x)

Once we have the equation from the previous step, we can solve it to find the inverse function, f-1(x). Let’s break it down:

  • Subtract 5 from both sides of the equation: x – 5 = 2f-1(x)
  • Divide both sides of the equation by 2: (x – 5) / 2 = f-1(x)

Therefore, the inverse function is f-1(x) = (x – 5) / 2.

Step 4: Verify the Inverse Function

It is important to verify the validity of the inverse function. To do so, we can apply the inverse formula to the original function and ensure that the result is the original input value. Let’s apply our inverse function to our original example:

  • Original function f(x) = 2x + 5
  • Apply f-1(x) to f(x): f-1(2x + 5) = (2x + 5 – 5) / 2 = x

As we can see, the result is x, which confirms that our inverse function is accurate.

Creating an inverse formula doesn’t have to be intimidating. By following these step-by-step instructions, you can create an inverse function that will help you find the original value before a given operation. Remember to understand the original formula, swap variables, solve for the inverse, and verify its accuracy. Now go ahead and apply this knowledge in your mathematical journey!

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