Understanding Inverse Functions

The video tutorial introduces inverse functions, explaining how they reverse the process of going from input to output. It provides examples of inverse operations like multiplication and division, and discusses how inverse functions are graphically represented as reflections over the line y = x. The tutorial also demonstrates how to find inverse functions by switching variables and solving for the new variable. Special cases, such as functions that do not have inverses, are also covered, with a focus on graphical representations and the horizontal line test.

What is the primary goal of an inverse function?

• To square the input value

• To double the input value

• To reverse the process from output back to input

• To add a constant to the input

Which of the following operations are inverses of each other?

• Multiplication and addition

• Addition and subtraction

• Squaring and cubing

• Division and subtraction

How are inverse functions represented graphically?

• As identical lines

• As parallel lines

• As perpendicular lines

• As reflections over the line y = x

In the intuitive approach, what is the first step to reverse the operation of multiplying by 5 and subtracting 10?

• Subtract 5

• Add 10

• Divide by 5

• Multiply by 10

What is the next step after adding 10 to both sides in the formal method of finding inverses?

• Multiply by 5

• Subtract 5

• Add 5

• Divide by 5

What is the inverse function of f(x) = x - 2 divided by 4?

• f inverse(x) = 4x + 2

• f inverse(x) = 4x - 2

• f inverse(x) = x/4 + 2

• f inverse(x) = x/4 - 2

Why does the function y = x^2 + 4 not have an inverse?

• It is a constant function

• It fails the horizontal line test

• It is a linear function

• It passes the vertical line test

How can we find the inverse of a function that fails the horizontal line test?

• By reflecting the graph over the x-axis

• By considering only a part of the graph

• By ignoring the graph

• By considering the entire graph

What is the inverse of the function y = x^2 + 4 for x ≥ 0?

• y = -√(x - 4)

• y = √(x + 4)

• y = √(x - 4)

• y = -√(x + 4)

When finding the inverse of a function, what is the significance of the line y = x?

• It is the line of rotation

• It is the line of translation

• It is the line of reflection

• It is the axis of symmetry