Finding the inverse of a rational function with a root as a denominator

The video tutorial explains how to find the inverse of a function. It begins by replacing F of X with Y to facilitate algebraic manipulation. The tutorial emphasizes the concept of inverse operations, which involve reversing the original operations applied to X. The process includes solving for Y by manipulating the equation, such as multiplying and dividing terms, and handling square roots. Finally, the inverse function is expressed in proper notation, completing the process.

What is the first step in finding the inverse of a function?

• Replace F(x) with Y

• Swap X and Y

• Multiply both sides by X

• Add 3 to both sides

Why do we swap the variables X and Y when finding an inverse function?

• To perform inverse operations

• To add constants

• To eliminate the square root

• To make the equation simpler

What operation is performed to eliminate the square root in the equation?

• Subtraction

• Addition

• Squaring both sides

• Multiplying by X

After isolating Y, what is the next step in finalizing the inverse function?

• Rewrite in inverse function notation

• Add 3 to both sides

• Divide by X

• Multiply by Y

What is the result of squaring both sides of the equation?

• The variables are swapped

• The equation becomes linear

• The square root is eliminated

• Y becomes X