Inverse Functions and Their Properties

Mr. Garrett explains inverse functions, emphasizing the importance of switching x and y. He demonstrates finding inverses using ordered pairs, graphs, and equations. The video covers graphical reflections over the line y=x and solving equations to find inverses. Verification of inverses through composition is also discussed. The session concludes with a mention of practice problems and future topics.

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

• Switching the coefficients

• Switching x and y

• Switching the exponents

• Switching the signs

When finding the inverse of a function using ordered pairs, what do you do?

• Divide each pair by 2

• Multiply each pair by 2

• Add 1 to each pair

• Switch the x and y values in each pair

How do you find the inverse of a function using a graph?

• Translate the graph up by 2 units

• Switch the x and y coordinates of each point

• Reflect the graph over the x-axis

• Rotate the graph 90 degrees

What is a characteristic of graphs of inverse functions?

• They are identical

• They are parallel to each other

• They are reflections over the line y = x

• They intersect at the origin

What happens to the graph of a function when you find its inverse?

• It rotates 180 degrees

• It reflects over the line y = x

• It shifts up

• It becomes a straight line

What is the first step in finding the inverse of an equation?

• Multiply both sides by 2

• Add 5 to both sides

• Switch x and y

• Divide both sides by 3

What is the result of switching x and y in the equation y = 2x + 3?

• x = 2y + 3

• y = 2x - 3

• x = 3y + 2

• y = 3x + 2

What is the inverse of the function f(x) = 2x + 3?

• f^-1(x) = (x - 3)/2

• f^-1(x) = 3x + 2

• f^-1(x) = 2x - 3

• f^-1(x) = x/2 + 3

What is the inverse of the function f(x) = 3x - 5?

• f^-1(x) = 5x - 3

• f^-1(x) = (x + 5)/3

• f^-1(x) = (x - 5)/3

• f^-1(x) = 3x + 5

What is the inverse of the function f(x) = 4x + 7?

• f^-1(x) = 7x + 4

• f^-1(x) = (x - 7)/4

• f^-1(x) = (x + 7)/4

• f^-1(x) = 4x - 7