Inverse Functions and Their Properties

The video tutorial explains how to find the inverse of a function, starting with a basic function f(x) = 2x + 3. It demonstrates the process of finding the inverse both conceptually and algebraically. Several examples are provided, including functions like 3x - 1, 5x + 8, and x/4 + 3. The tutorial also includes practice problems to reinforce the concepts learned.

What is the function f(x) described in the introduction?

• f(x) = x/2 + 3

• f(x) = 2x - 3

• f(x) = 2x + 3

• f(x) = 3x + 2

What operation is performed first when finding the inverse of f(x) = 2x + 3?

• Divide by 2

• Add 3

• Multiply by 2

• Subtract 3

How do you algebraically find the inverse of a function?

• Divide by 2

• Add 3

• Multiply by 2

• Switch x and y, then solve for y

What is the inverse of f(x) = 3x - 1?

• f inverse(x) = x/3 - 1

• f inverse(x) = (x + 1)/3

• f inverse(x) = 3x + 1

• f inverse(x) = (x - 1)/3

What is the value of f inverse(5) for f(x) = 3x - 1?

• 4

• 5

• 2

• 3

What is the inverse of f(x) = 5x + 8?

• f inverse(x) = (x - 8)/5

• f inverse(x) = 5x - 8

• f inverse(x) = (x + 8)/5

• f inverse(x) = 5x + 8

What is the value of f inverse(-2) for f(x) = 5x + 8?

• -2

• -5

• -3

• -4

What is the inverse of f(x) = x/4 + 3?

• f inverse(x) = x/4 - 3

• f inverse(x) = 4(x - 3)

• f inverse(x) = (x + 3)/4

• f inverse(x) = 4x + 3

What is the solution to f(x) = f inverse(x) for f(x) = x/4 + 3?

• x = 4

• x = 2

• x = 3

• x = 1

What is the inverse of f(x) = 2(3x + 1)?

• f inverse(x) = 6x + 2

• f inverse(x) = (x - 2)/6

• f inverse(x) = (x + 2)/6

• f inverse(x) = 6x - 2