How to find the inverse of a direct variation function

The video tutorial explains how to find the inverse of a function. It begins with an introduction to inverse functions and their significance. The instructor discusses graphing functions, specifically G(x) and y, and highlights their similarities. The video then delves into the special relationships between functions and their output values. A step-by-step process is provided to find the inverse of a function, including replacing, swapping, and solving variables. The tutorial concludes with a discussion on inverse function notation, emphasizing the importance of understanding these concepts.

What is the primary difference between graphing G(x) and y, according to the video?

• The functions have different rules.

• The input values are different.

• The output values are different.

• The graphs are completely different.

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

• Graph the function.

• Replace the function name with y.

• Solve for y.

• Swap the x and y variables.

After swapping the x and y variables, what is the next step in finding the inverse?

• Replace y with the inverse notation.

• Swap the variables again.

• Graph the new function.

• Solve for y.

How is the inverse of a function typically denoted?

• Function name with a tilde symbol.

• Function name raised to the negative first power.

• Function name with a prime symbol.

• Function name raised to the second power.

What is the inverse of the function G(x) = 5x?

• G inverse of x = 5/x

• G inverse of x = x + 5

• G inverse of x = x/5

• G inverse of x = 5x