Finding Inverses of Functions

The video tutorial explains how to find the inverse of a given one-to-one function. It begins by defining inverse functions and highlighting the interchange of inputs and outputs. The tutorial emphasizes that a function and its inverse undo each other but warns against common misconceptions. It provides a step-by-step process to find the inverse, including interchanging variables and solving for y, concluding with the final step of replacing y with the inverse function notation.

What is the primary characteristic of a function and its inverse?

• They undo each other.

• They have the same range.

• They have the same graph.

• They have the same domain.

What is a common mistake when finding the inverse of the function f(x) = 2x - 5?

• Assuming the inverse is x / 2 + 5.

• Interchanging x and y incorrectly.

• Forgetting to solve for y.

• Using the wrong function definition.

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

• Solve for x.

• Replace f(x) with y.

• Graph the function.

• Find the domain.

After interchanging x and y, what is the next step in finding the inverse function?

• Add 5 to both sides.

• Subtract 5 from both sides.

• Multiply both sides by 2.

• Divide both sides by 2.

What is the final expression for the inverse of the function f(x) = 2x - 5?

• y = 2x + 5

• y = x / 2 - 5

• y = x / 2 + 5

• y = 2x - 5