Inverse Operations and Functions

The video tutorial explains the concept of inverse functions, which are the opposite of a given function and return the input value. It provides a step-by-step process to find the inverse of a function by switching the x and y variables and rearranging the equation. The tutorial includes practice problems for viewers to apply the method and concludes with a summary of key points about inverse functions.

What is the inverse operation of addition?

• Division

• Multiplication

• Subtraction

• Exponentiation

What does the inverse of a function do?

• It multiplies the function by a constant

• It adds a constant to the function

• It reverses the function's effect

• It squares the function

In the function machine example, what operation is performed first?

• Multiply by 5

• Divide by 5

• Add 2

• Subtract 2

What is the result of adding 2 to 13 and then dividing by 5?

• 4

• 2

• 5

• 3

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

• Divide by a constant

• Switch x and y variables

• Multiply by a constant

• Add a constant

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

• Rearrange to make y the subject

• Multiply by a constant

• Add a constant

• Divide by a constant

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

• f^(-1)(x) = 3x - 2

• f^(-1)(x) = (x - 2) / 3

• f^(-1)(x) = x + 2

• f^(-1)(x) = 2x + 3

What is the inverse function of f(x) = 4/3x + 2/3?

• f^(-1)(x) = 4/3x - 2/3

• f^(-1)(x) = 4/3x + 2/3

• f^(-1)(x) = 3/4x + 2/3

• f^(-1)(x) = 3/4x - 2/3

What is the domain restriction mentioned in the final example?

• x > 3

• x < 0

• x < 3

• x > 0

What is the inverse function of f(x) = x^2 + 3, given the domain restriction?

• f^(-1)(x) = x^2 + 3

• f^(-1)(x) = sqrt(x + 3)

• f^(-1)(x) = x^2 - 3

• f^(-1)(x) = sqrt(x - 3)