Finding a Function’s Inverse Algebraically

The video tutorial explains inverse functions, starting with simple examples and moving to more complex cases. It covers the algebraic process of finding inverses, verifying them through composition, and handling non-one-to-one functions by restricting their domain. The tutorial uses functions F, G, and H to illustrate these concepts, emphasizing the importance of the vertical and horizontal line tests in determining if a function has an inverse.

What is the inverse of the function F(x) = x - 1?

• F^-1(x) = x / 1

• F^-1(x) = x - 1

• F^-1(x) = x + 1

• F^-1(x) = x * 1

Which step is NOT part of finding the inverse of G(x) = sqrt(3x + 2)?

• Replace G(x) with Y

• Add 2 to both sides

• Switch X and Y

• Square both sides

What is the inverse of G(x) = sqrt(3x + 2)?

• G^-1(x) = (x^2 - 2) / 3

• G^-1(x) = (x^2 + 2) / 3

• G^-1(x) = (x^2 - 3) / 2

• G^-1(x) = (x^2 + 3) / 2

What is the result of the composition G(G^-1(x)) for the function G(x) = sqrt(3x + 2)?

• sqrt(x)

• 3x + 2

• x^2

• x

What is the purpose of the horizontal line test in the context of inverse functions?

• To determine if a function is continuous

• To check if a function is one-to-one

• To ensure a function is integrable

• To verify if a function is differentiable

Why is it necessary to restrict the domain of H(x) = 3x^2 + 1 to find its inverse?

• To make the function continuous

• To simplify the function

• To ensure the function is one-to-one

• To make the function pass the vertical line test

What is the domain restriction for the inverse of H(x) = 3x^2 + 1?

• x <= 1

• x >= 1

• x > 1

• x < 1