Inverse Functions and Their Properties

Mrs. A introduces the concept of inverse functions, explaining how to find them by reflecting over the line y=x. She demonstrates the algebraic process of switching variables and solving for the new dependent variable. The video includes a step-by-step guide to finding the inverse of a linear function, substituting values into the inverse equation, and evaluating complex expressions using both the original and inverse functions.

What is the purpose of finding the inverse of a function?

• To simplify the function

• To make the function more complex

• To change the function's domain

• To reflect the function over the line y = x

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

• Graph the function

• Add a constant to the function

• Multiply the function by a factor

• Switch the independent and dependent variables

After switching the variables, what is the next step in finding the inverse?

• Multiply both sides by a factor

• Graph the new equation

• Solve for the new dependent variable

• Add a constant to both sides

What operation is performed to isolate the dependent variable in the inverse function?

• Addition

• Division

• Subtraction

• Multiplication

What is the inverse of the function f(x) = 2x + 7?

• y = 2(x - 7)

• y = 2x - 7

• y = (x + 7) / 2

• y = (x - 7) / 2

What is the result of substituting x = 3 into the inverse function?

• -2

• -1

• 2

• 1

When evaluating a complex expression, which function is used with x = 4?

• The inverse function

• The original function

• A quadratic function

• A constant function

What is the result of substituting x = 5 into the inverse function?

• 0

• -1

• -2

• 1

What is the final value of the complex expression evaluated in the video?

• 0

• -3

• -30

• -33