How to find the inverse of a rational function and verify it's inverse

The video tutorial explains how to find and verify inverse functions. It begins by introducing the concept of inverse functions and the importance of switching the input and output values. The process involves changing F of X to Y, interchanging X and Y, and solving for Y. The tutorial also covers verifying the inverse by checking if the composition of the function and its inverse equals X. The explanation includes algebraic steps and examples to ensure understanding.

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

• Change F of X to Y

• Multiply by 5

• Divide by X

• Add 1 to both sides

Why do we interchange X and Y when finding the inverse?

• To add constants

• To eliminate fractions

• To switch the domain and range

• To simplify the equation

What operation is performed to eliminate the fraction when solving for Y?

• Subtract X from both sides

• Divide by 5

• Add 1 to both sides

• Multiply by 5/1

What is the inverse function derived in the video?

• F inverse of X = 5X - 1

• F inverse of X = X/5 + 1

• F inverse of X = X - 5

• F inverse of X = 5X + 1

How do we verify that two functions are inverses of each other?

• By ensuring their compositions equal X

• By comparing their domains

• By checking if their graphs intersect

• By solving for Y in both functions