Inverse Functions and Their Properties

The video tutorial explains the process of finding the inverse of a parabola, which is not a one-to-one function. It highlights the issue of the inverse not being a function and the need to restrict the domain to make it a function. The tutorial demonstrates how to find the inverse algebraically by swapping variables and solving for y, and discusses the importance of the vertical line test. It also covers how the domain and range of the inverse function are reversed compared to the original function.

Why is finding the inverse of a parabola problematic?

• Because it results in a non-function

• Because it does not have a domain

• Because it is already an inverse

• Because it is always a one-to-one function

What is the purpose of restricting the domain of a parabola?

• To eliminate the need for an inverse

• To make it a two-to-one function

• To make it a zero-to-one function

• To make it a one-to-one function

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

• Dividing by a constant

• Swapping X and Y

• Adding a constant

• Multiplying by a factor

Why do we need to include a plus or minus sign when finding the inverse?

• Because of the square root property

• Because of the cube root property

• Because of the logarithmic property

• Because of the exponential property

What does the graph of the inverse function resemble before domain restriction?

• A hyperbola

• A straight line

• A circle

• A sideways parabola

What test does the inverse function fail, indicating it is not a function?

• Curved line test

• Vertical line test

• Horizontal line test

• Diagonal line test

What happens to the inverse function after restricting the domain of the original function?

• It becomes a function

• It becomes a relation

• It becomes undefined

• It becomes a constant

What disappears from the inverse function after domain restriction?

• The right arm

• The left arm

• The top arm

• The bottom arm

How is the inverse function related to the original function graphically?

• It is a reflection over the line Y = X

• It is a reflection over the line Y = Y

• It is a reflection over the line X = Y

• It is a reflection over the line X = X

What happens to the domain and range when the inverse is found?

• They are halved

• They are doubled

• They remain the same

• They are swapped