Finding Inverse Functions Steps

The video tutorial explains how to find the inverse of a function by first replacing f(x) with y and swapping the x and y variables. It then demonstrates algebraic manipulation to solve for y, including multiplying and distributing terms. The tutorial provides two methods to solve the equation, emphasizing the importance of isolating y. The video concludes with a summary and addresses any questions.

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

• Multiply by the denominator

• Add 3x to both sides

• Swap the variables

• Replace f(x) with y

Why do we replace f(x) with y when finding the inverse?

• To eliminate variables

• To change the function type

• To simplify the math

• To make the graph easier to draw

What happens to the x and y coordinates when finding the inverse?

• They are multiplied

• They are swapped

• They are added

• They are divided

What should you do if y is in the denominator when solving for y?

• Multiply by y minus 3

• Add y to both sides

• Subtract y from both sides

• Divide by y

What is the purpose of multiplying by y minus 3 in the equation?

• To eliminate y from the equation

• To solve for x

• To clear the denominator

• To add a constant

What is the first algebraic step after swapping variables?

• Divide by x

• Distribute y

• Multiply by y minus 3

• Add 3x to both sides

What is the result of distributing y in the equation yx - 3x = 1?

• yx + 3x = 1

• yx - 3x = 0

• yx = 1 + 3x

• yx - 3x = 1

How can you solve the equation yx - 3x = 1 for y?

• Multiply both sides by 3x

• Divide both sides by y

• Subtract 3x from both sides and multiply by x

• Add 3x to both sides and divide by x

What does the equation yx - 3x = 1 represent in the process?

• The final solution

• An intermediate step

• The inverse function

• The original function

What is an alternative method to solve for y in the equation yx - 3x = 1?

• Add 3x to both sides

• Factor out x and divide by x

• Multiply by y

• Subtract 1 from both sides