Understanding Functions and Their Inverses

The video tutorial explains how to determine the domain and range of a function f(x) = (x + 2)^2 to ensure it is increasing and one-to-one. It discusses the importance of restricting the domain to achieve this and uses interval notation to express the domain and range. The tutorial also covers finding the inverse of the function and determining its domain and range. Finally, it verifies the results graphically, showing the symmetry of the function and its inverse across the line y = x.

What is the initial function given in the video?

• f(x) = x^2 + 2

• f(x) = (x - 2)^2

• f(x) = (x + 2)^2

• f(x) = x^2 - 2

Why is it necessary to restrict the domain of the function?

• To make the function periodic

• To make the function decreasing

• To make the function one-to-one

• To make the function constant

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

• [-2, ∞)

• (-2, ∞)

• [0, ∞)

• (-∞, 2]

What is the range of the restricted function in interval notation?

• (-∞, 0]

• [0, ∞)

• (-2, ∞)

• [2, ∞)

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

• Add 2 to both sides

• Interchange x and y

• Subtract 2 from both sides

• Square both sides

What is the inverse function of f(x) = (x + 2)^2?

• f^(-1)(x) = x^2 + 2

• f^(-1)(x) = x^2 - 2

• f^(-1)(x) = √(x) + 2

• f^(-1)(x) = √(x) - 2

What is the domain of the inverse function?

• [2, ∞)

• (-∞, 0]

• [0, ∞)

• (-2, ∞)

What is the range of the inverse function?

• [2, ∞)

• [0, ∞)

• (-∞, 0]

• (-2, ∞)

How are the graphs of the function and its inverse related?

• They are parallel

• They are identical

• They are perpendicular

• They are symmetrical across the line y = x

What does it mean for a function to be one-to-one?

• It is increasing

• It passes the horizontal line test

• It is constant

• It is decreasing