Inverse Functions and Their Properties

This tutorial continues the exploration of inverse functions, focusing on cubic functions. It begins with a visual representation of a cubic function and explains the horizontal line test to verify if a function is one-to-one. The video then demonstrates how to derive the inverse of a cubic function algebraically. Using a calculator, the tutorial shows how to graphically verify the inverse function's symmetry with the original function. Finally, it tests the inverse function with specific inputs to confirm its accuracy. The video concludes with a call to action for social media engagement.

What is the purpose of the horizontal line test in relation to inverse functions?

• To determine if a function is continuous

• To check if a function is differentiable

• To verify if a function is one-to-one

• To find the maximum value of a function

What is the first step in finding the inverse of a function given in f(x) notation?

• Swap x and y

• Convert f(x) to y

• Take the derivative

• Graph the function

After swapping x and y in the function, what is the next step to find the inverse?

• Take the square root

• Solve for x

• Solve for y

• Differentiate the function

What is the line of symmetry for a function and its inverse on a graph?

• y = 0

• x = y

• y = x

• x = 0

Why might a graph not appear symmetrical when plotted on a calculator?

• The calculator is malfunctioning

• The zoom settings are incorrect

• The function is not one-to-one

• The function is not continuous

What is the significance of the line y = x in the context of inverse functions?

• It is the tangent line

• It is the line of symmetry

• It is the axis of rotation

• It is the line of best fit

What should you do if the graph of a function and its inverse does not appear symmetrical?

• Ignore the graph

• Recalculate the inverse

• Adjust the zoom settings

• Change the function

What should be the output of an inverse function if the input is the output of the original function?

• The square of the input

• The input of the original function

• The reciprocal of the input

• The derivative of the original function

If the original function's input is 8 and the output is 1728, what should be the input for the inverse function to get an output of 8?

• 1.25

• 144

• 1728

• 8

What is the output of the original function if the input is 1.25?

• 1728

• 1.25

• 8

• 144.7