Exploring Inverse Functions and Relations

This video tutorial covers inverse functions and relations, explaining the difference between them and how to find and graph inverses. It includes examples of ordered pairs and their inverses, function notation, and the process of finding inverses. The tutorial also discusses identity functions and how to verify if two functions are inverses of each other.

What is the main difference between a relation and a function?

• A function is a set of ordered pairs, while a relation is a set of unordered pairs.

• A relation is a set of ordered pairs, while a function is a set of unordered pairs.

• A function is a set of ordered pairs, while a relation is a function that passes the horizontal line test.

• A relation is a set of ordered pairs, while a function is a relation that passes the vertical line test.

How do you find the inverse of an ordered pair (a, b)?

• Subtract 1 from both a and b.

• Add 1 to both a and b.

• Switch the positions of a and b.

• Switch the signs of a and b.

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

• f(x)^-1

• f(x^-1)

• f^-1x

• f^-1(x)

What does the graph of an inverse function represent?

• A rotation by 90 degrees

• A reflection over the line y=x

• A reflection over the y-axis

• A reflection over the x-axis

What is the first step in finding the inverse of a function f(x)?

• Solve for y.

• Rewrite f(x) as y.

• Switch the x and y variables.

• Graph the function.

After switching the x and y variables in the equation, what is the next step to find the inverse?

• Rewrite f(x) as y.

• Switch the x and y variables again.

• Graph the function.

• Solve for y.

How do you graph the inverse of a linear function?

• Rotate it by 180 degrees.

• Reflect it over the x-axis.

• Reflect it over the y-axis.

• Reflect it over the line y=x.

What is the inverse of the function y = -12x + 1?

• y = 2x + 2

• y = -2x + 2

• y = 2x - 2

• y = -2x - 2

What is the inverse of the quadratic function y = 3x^2?

• y = ±√(3x)/3

• y = ±√(x/3)

• y = ±√(3/x)

• y = ±√(x)/3

How can you verify if two functions are inverses of each other?

• Check if f(g(x)) = 0 and g(f(x)) = 0

• Check if f(g(x)) = 1 and g(f(x)) = 1

• Check if f(g(x)) = x and g(f(x)) = x

• Check if f(g(x)) = y and g(f(x)) = y