Inverse Functions

The video tutorial explains inverse functions, starting with the basic concept that an inverse function reverses the operations of the original function. It covers how to find inverse functions using algebra, the properties of inverse functions, and how to verify them mathematically. The tutorial includes examples and practice problems, demonstrating the process of swapping variables and solving for the inverse. It also discusses the graphical representation of inverse functions, highlighting the reflection across the line y = x.

What is the main purpose of an inverse function?

• To double the output of the original function

• To reverse the operations of the original function

• To find the reciprocal of the original function

• To square the output of the original function

How do you find the inverse of a function algebraically?

• Swap x and y, then solve for y

• Add 5 to the function

• Multiply the function by 2

• Divide the function by 3

What is the relationship between the domain of a function and the range of its inverse?

• They are unrelated

• The domain of the inverse is twice the range of the function

• The domain of the function is the range of its inverse

• They are always equal

Which of the following is a method to verify if two functions are inverses?

• Check if their graphs intersect

• Ensure their compositions equal the identity function

• Add their outputs

• Multiply their outputs

What is the inverse of the function f(x) = 4x - 5?

• f inverse(x) = 4x + 5

• f inverse(x) = (x + 5) / 4

• f inverse(x) = (x - 5) / 4

• f inverse(x) = 4x - 5

How do you find the inverse of a cubic function like x^3 + 1?

• Add 1 and take the square root

• Subtract 1 and take the cube root

• Subtract 1 and take the square root

• Add 1 and take the cube root

What geometric transformation represents finding the inverse of a function?

• Rotation around the origin

• Reflection across the line y = x

• Translation along the x-axis

• Scaling by a factor of 2