Exploring Inverse Functions in Algebra 2

This video tutorial covers inverse functions, explaining their definition and purpose. It provides a step-by-step guide to finding inverses algebraically, including changing notation and solving equations. The tutorial includes several example problems to illustrate the process. Additionally, it explains how to verify if two functions are inverses using compositions, ensuring both compositions equal the original variable.

What is the first step in finding an inverse function algebraically?

• Switch x and y in the equation

• Solve for y

• Take the square root of both sides

• Change f(x) to y

What is the correct notation for the inverse of f(x)?

• inverse f(x)

• f-1(x)

• f inverse(x)

• f(x) inverse

After switching x and y in the equation, what should you do next?

• Subtract 4 from both sides

• Change f(x) to y

• Solve for y

• Change the notation to f inverse of x

What is the inverse of f(x) = x + 4?

• f inverse of x = x / 4

• f inverse of x = 4 - x

• f inverse of x = x + 4

• f inverse of x = x - 4

What is the inverse of a(x) = 2x - 1?

• Inverse of a(x) = x / 2 - 1/2

• Inverse of a(x) = 2x + 1

• Inverse of a(x) = 1/2 x + 1/2

• Inverse of a(x) = x - 2

What is the inverse of h(x) = x^2 + 3?

• h inverse(x) = sqrt(x + 3)

• h inverse(x) = sqrt(x) + 3

• h inverse(x) = sqrt(x - 3)

• h inverse(x) = x^2 - 3

For the function g(x) = cube root of x + 2, what is the inverse?

• Inverse of g(x) = x + 2 cubed

• Inverse of g(x) = cube root of (x - 2)

• Inverse of g(x) = (x - 2)^3

• Inverse of g(x) = x^3 - 2

How do you verify if two functions are inverses using compositions?

• Both compositions must equal x

• Both compositions must equal 1

• Both compositions must equal 0

• Both compositions must equal y

If f(g(x)) = x, what can be inferred about f(x) and g(x)?

• They are identical

• They are inverses

• They are not related

• They are complementary

What does it mean if g(f(x)) = x for two functions f and g?

• f and g are inverses

• f and g are identical

• f and g are quadratic

• f and g have no relation