How to determine the inverse of a rational function

The video tutorial guides students through solving an algebraic equation by replacing variables, swapping coordinates, and simplifying expressions. It emphasizes the importance of following a structured process, especially when dealing with variables in the denominator. The tutorial concludes with factoring and dividing to isolate the variable Y, ultimately finding the inverse function.

Why is it suggested to replace F(x) with Y in algebraic manipulations?

• To make the equation more visually appealing

• To simplify the algebraic manipulation

• To confuse the students

• To change the function's meaning

What is the first step in representing a reflection over the line Y = X?

• Multiply by the reciprocal

• Subtract 2 from both sides

• Swap the X and Y coordinates

• Add 3 to both sides

What is a common difficulty students face when solving equations with variables in the denominator?

• Solving for a variable in the denominator

• Using the quadratic formula

• Combining like terms

• Forgetting to add constants

What property is applied to simplify the expression YX - 2X = Y + 3?

• Distributive property

• Identity property

• Associative property

• Commutative property

How do you isolate Y when you have two Y terms in an equation?

• Multiply by the reciprocal

• Use the quadratic formula

• Factor out Y

• Add them together

What is the final expression for the inverse function in the given problem?

• Y = (3X + 2) / (X - 2)

• Y = (2X + 3) / (X + 1)

• Y = (X + 3) / (2X - 1)

• Y = (3 + 2X) / (X - 1)

What is the purpose of dividing by X - 1 in the final step?

• To change the equation's form

• To simplify the equation

• To isolate the variable Y

• To eliminate the variable X