Inverse Functions and Their Properties

The video tutorial explains how to find the inverse of a given function, determine its domain and range, and verify the results graphically. It begins by identifying the domain and range of the original function using interval notation. The process of finding the inverse function involves interchanging variables and solving the resulting equation. The tutorial also covers how to determine the domain and range of the inverse function and concludes with a graphical verification to ensure the function and its inverse are reflections across the line y = x.

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

• Interchange x and y

• Replace f(x) with y

• Solve for x

• Graph the function

Why must the expression under the square root be non-negative?

• To ensure the result is real

• To simplify the equation

• To make the function continuous

• To find the range

What is the domain of the given function in interval notation?

• [3/5, ∞)

• (-∞, 3/5]

• [0, ∞)

• (-∞, 0]

What is the range of the given function?

• [3/5, ∞)

• (-∞, 0]

• (-∞, 3/5]

• [0, ∞)

What is the inverse function of f(x) = √(5x - 3)?

• 5√(x - 3)

• 5x^2 - 3

• (x^2 + 3)/5

• √(x^2 + 3)

What is the domain of the inverse function?

• (-∞, 3/5]

• (-∞, 0]

• [0, ∞)

• [3/5, ∞)

What is the range of the inverse function?

• [3/5, ∞)

• (-∞, 3/5]

• [0, ∞)

• (-∞, 0]

Why is it important to determine the domain and range of the inverse function?

• To find the maximum value

• To make the function continuous

• To simplify the function

• To ensure the graph is a reflection across y = x

What would happen if the domain restriction for the inverse function was not applied?

• The graph would be an entire parabola

• The function would be undefined

• The range would be incorrect

• The domain would be incorrect

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

• It is the line of reflection for the function and its inverse

• It is the axis of symmetry for the function

• It represents the domain of the function

• It is the range of the inverse function