Understanding Inverse Functions

The video tutorial explains how to determine if two linear functions are inverses of each other. It begins by discussing the operations of the functions and the concept of inverse functions. The tutorial then demonstrates how to verify if functions are inverses by using composition and checking if f(g(x)) equals x and g(f(x)) equals x. It also highlights the graphical representation of functions as reflections across the line y = x. The tutorial concludes by showing that the given functions are not inverses, both algebraically and graphically.

What is the main purpose of inverse functions?

• To add a constant to inputs

• To reflect functions across the x-axis

• To multiply inputs by a constant

• To undo the operations of another function

What are the given functions f(x) and g(x) in the video?

• f(x) = 5x + 2, g(x) = x/5 - 2

• f(x) = 2x + 5, g(x) = x/2 - 5

• f(x) = 4x + 3, g(x) = x/4 - 3

• f(x) = 3x + 4, g(x) = x/3 - 4

What must be true for two functions to be inverses?

• f(g(x)) = y and g(f(x)) = y

• f(g(x)) = 1 and g(f(x)) = 1

• f(g(x)) = 0 and g(f(x)) = 0

• f(g(x)) = x and g(f(x)) = x

What is the first step in checking if f and g are inverses?

• Multiply the functions

• Graph the functions

• Calculate f(g(x))

• Calculate g(f(x))

What is the result of simplifying f(g(x))?

• 0

• x - 9

• x

• x + 9

Why are f and g not inverses based on f(g(x))?

• Because f(g(x)) equals x + 9

• Because f(g(x)) equals x - 9

• Because f(g(x)) equals 0

• Because f(g(x)) equals x

What is the graphical method to check if two functions are inverses?

• Check if they are reflections across the origin

• Check if they are reflections across the line y = x

• Check if they are reflections across the y-axis

• Check if they are reflections across the x-axis

How are the functions f(x) and g(x) represented on the graph?

• f(x) in red, g(x) in blue

• f(x) in red, g(x) in green

• f(x) in green, g(x) in red

• f(x) in blue, g(x) in red

What does the graph show about the relationship between f(x) and g(x)?

• They are inverses of each other

• They are not inverses of each other

• They are identical functions

• They are perpendicular to each other

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

• It is the axis of symmetry for inverse functions

• It is the line where functions intersect

• It is the line where functions are parallel

• It is the line where functions are perpendicular