Understanding Inverses of Functions

The video tutorial on Khan Academy explains the concept of inverses of functions. It begins with an introduction to the exercise, which involves moving a line to understand the graph of h(x) and its inverse. The tutorial demonstrates how to map points from h(x) to its inverse by swapping x and y values. It then shows how to graph the inverse using endpoints and explains the reflection of the graph around the line y=x. The tutorial concludes with a summary of the process of graphing the inverse of a function.

What is the primary focus of the Khan Academy exercise discussed in the video?

• Understanding derivatives of functions

• Understanding inverses of functions

• Understanding limits of functions

• Understanding integrals of functions

What is the simplest way to determine the inverse of a function according to the video?

• By solving the function for zero

• By finding the derivative

• By mapping points from h(x) to h inverse of x

• By integrating the function

If h(x) maps -8 to 1, what should h inverse of x map according to the video?

• 1 to -8

• 3 to -4

• -8 to 1

• -4 to 3

What is the inverse mapping for the point where h(x) maps 3 to -4?

• -8 to 1

• -4 to 3

• 3 to -4

• 1 to -8

What is another way to think about the inverse of a function as mentioned in the video?

• As a translation along the x-axis

• As a scaling transformation

• As a reflection over the line y = x

• As a rotation around the origin

What happens to the graph of a function when it is reflected over the line y = x?

• It becomes a vertical line

• It becomes the inverse of the original function

• It becomes a horizontal line

• It remains unchanged

What is the relationship between the x and y values in the inverse of a function?

• They are multiplied by each other

• They are swapped

• They are subtracted from each other

• They are added together

What is the final step in graphing the inverse of a function as described in the video?

• Finding the derivative

• Drawing a tangent line

• Reflecting over the line y = x

• Calculating the integral