Understanding Functions and Their Inverses

The video tutorial explains how to determine the domain and range of a function involving a square root, and how to find its inverse. It covers the importance of the radicand being non-negative for real values, and uses interval notation to express the domain and range. The tutorial also demonstrates graphing the function to verify these values. It then explains the process of finding the inverse function, including interchanging variables and solving for y. Finally, it verifies the inverse function graphically, showing symmetry across the line y = x.

What is the domain of the function f(x) = √(2x - 1) - 3?

• x > 1/2

• x ≥ 0

• x ≥ 1

• x ≥ 1/2

In interval notation, how is the domain of f(x) = √(2x - 1) - 3 expressed?

• (1/2, ∞)

• [1/2, ∞)

• [0, ∞)

• (0, ∞)

What is the range of the function f(x) = √(2x - 1) - 3?

• y > 0

• y > -3

• y ≥ -3

• y ≥ 0

How is the range of f(x) = √(2x - 1) - 3 expressed in interval notation?

• (-3, ∞)

• (-∞, -3]

• [-3, ∞)

• [0, ∞)

What happens to the domain of a function when finding its inverse?

• It remains the same.

• It is not related to the inverse function.

• It becomes the domain of the inverse function.

• It becomes the range of the inverse function.

What is the first step in finding the inverse of f(x) = √(2x - 1) - 3?

• Add 3 to both sides.

• Subtract 3 from both sides.

• Square both sides.

• Divide by 2.

What is the domain of the inverse function of f(x) = √(2x - 1) - 3?

• x > 1/2

• x ≥ -3

• x ≥ 1/2

• x > -3

How is the domain of the inverse function expressed in interval notation?

• (1/2, ∞)

• [1/2, ∞)

• [-3, ∞)

• (-3, ∞)

What should be true about the graphs of a function and its inverse?

• They should be parallel.

• They should intersect at the origin.

• They should be symmetrical across the line y = x.

• They should be identical.

What does the graphical verification of the inverse function confirm?

• The function is not invertible.

• The function is linear.

• The function and its inverse are symmetrical across y = x.

• The function is quadratic.