Understanding Finite Functions and Invertibility

The video tutorial explains the concept of a finite function f with a domain of letters a to e and its corresponding range. It demonstrates how to build a mapping diagram for the function and discusses the conditions for a function to be invertible. The tutorial provides an example of a non-invertible function where multiple domain elements map to the same range element, and contrasts it with an invertible function where each domain element maps to a unique range element.

What is the output of the function f when the input is 'b'?

• 9

• 2

• 3

• -6

Which input value maps to the output -6 in the function f?

• d

• e

• b

• a

What is the purpose of building a mapping diagram for a function?

• To find the domain of the function

• To pair each domain element with its correct range element

• To determine the function's range

• To calculate the function's inverse

Why is the function f not invertible?

• It has no range

• It maps multiple domain elements to the same range element

• It has no domain

• It maps each domain element to a unique range element

In the new example, what does the input 'c' map to?

• -36

• 9

• 49

• -4

What is the output of the inverse function when the input is 49?

• b

• c

• a

• d

What is the output of the inverse function when the input is -36?

• d

• a

• b

• c

Which of the following mappings ensures a function is invertible?

• One-to-one

• None of the above

• One-to-many

• Many-to-one

What is a key characteristic of a one-to-one mapping?

• Each range element maps to a unique domain element

• Each domain element maps to multiple range elements

• Each range element maps to multiple domain elements

• Each domain element maps to a unique range element

In the context of functions, what does 'invertible' mean?

• The function maps each domain element to multiple range elements

• The function has no domain

• The function can be reversed to map range elements back to domain elements

• The function has no range