Inverse Functions and Their Properties

The video tutorial explains how to determine if two linear functions are inverses of each other. It covers both algebraic and graphical methods for verification. Algebraically, it demonstrates that if f(g(x)) = x and g(f(x)) = x, the functions are inverses. Graphically, it shows that inverse functions are reflections across the line y = x. The tutorial provides step-by-step instructions for both methods, ensuring a comprehensive understanding of the concept.

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

• f(x) = 2x - 5 and g(x) = 2x + 5

• f(x) = 2x - 5 and g(x) = 1/2x + 5/2

• f(x) = x^2 - 5 and g(x) = 1/2x + 5

• f(x) = 2x + 5 and g(x) = 1/2x - 5/2

What is the condition for two functions to be inverses of each other?

• f(g(x)) = x and g(f(x)) = x

• f(g(x)) = g(x) and g(f(x)) = f(x)

• f(g(x)) = 0 and g(f(x)) = 0

• f(g(x)) = 1 and g(f(x)) = 1

What is the first step in verifying f(g(x)) algebraically?

• Graph the functions

• Solve for x

• Substitute f(x) into g(x)

• Substitute g(x) into f(x)

What is the result of f(g(x)) after simplification?

• 2x

• x

• 5

• 0

What is the first step in verifying g(f(x)) algebraically?

• Graph the functions

• Substitute g(x) into f(x)

• Substitute f(x) into g(x)

• Solve for y

What is the result of g(f(x)) after simplification?

• 0

• 5

• 2x

• x

How are the graphs of f(x) and g(x) related if they are inverses?

• They intersect at the origin

• They are identical

• They are reflections across the line y = x

• They are parallel lines

What color is used to graph f(x) in the video?

• Yellow

• Blue

• Red

• Green

What color is used to graph g(x) in the video?

• Green

• Red

• Yellow

• Blue

What conclusion is drawn about the functions f(x) and g(x)?

• They are parallel

• They are inverses of each other

• They are not related

• They are identical