Inverse Functions and Domain Determination

The video tutorial explains how to find the inverse, domain, and range of radical functions. It begins with an introduction to the topic, followed by detailed steps to determine the domain by equating the expression inside the radical to zero and testing values on a number line. The process of finding the inverse involves replacing f(x) with y, interchanging x and y, and solving for the new y. The range is determined from the inverse function, considering the absence of variables in the denominator. An example is provided to illustrate these concepts, and the video concludes with a summary of the methods discussed.

How do you determine the domain of a radical function?

• By solving for y

• By equating the expression inside the radical to zero

• By finding the range of the function

• By interchanging x and y

What is the result of solving x - 4 = 0?

• x = -4

• x = 0

• x = 2

• x = 4

What is the critical point for the function x - 4?

• x = 2

• x = -4

• x = 4

• x = 0

Why do we test numbers before and after the critical point on a number line?

• To determine if the function is increasing or decreasing

• To find the inverse of the function

• To find the range of the function

• To check which values are part of the domain

What is the domain of the radical function x - 4?

• [4, ∞)

• (-∞, ∞)

• [0, ∞)

• (-∞, 4]

What is the purpose of testing numbers before and after the critical point?

• To determine the range

• To solve for y

• To find the inverse

• To check the domain

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

• Solve for y

• Interchange x and y

• Replace f(x) with y

• Equate the expression inside the radical to zero

What happens when you interchange x and y in the process of finding the inverse?

• You solve for the new y

• The function becomes undefined

• The domain and range are swapped

• The function remains the same

What is the purpose of taking the square of both sides when finding the inverse?

• To interchange x and y

• To determine the range

• To find the domain

• To eliminate the radical

What is the next step after replacing f(x) with y in finding the inverse?

• Determine the range

• Find the domain

• Interchange x and y

• Solve for x