121 Week 3 - Functions

Question 1

Function

Answer 1

A type of binary relation that associates each element in a set with a single element of another set.

Question 2

Domain

Answer 2

A set of all input elements

Question 3

Codomain

Answer 3

A set of all possible outputs

Question 4

Range

Answer 4

A set of all outputs

Question 5

Image

Answer 5

An element that is an output of a function

Question 6

Preimage

Answer 6

An element that is an input to a function

Question 7

Inverse function

Answer 7

A function that reverses the effects of the original function.
You can find the inverse by reversing all the operations of the original function.
Only bijective functions can have an inverse function.

Question 8

Bijective function

Answer 8

A function that is both injective and surjective

Question 9

Surjective function

Answer 9

The co-domain and range of a function must be the same.
Every element in the codomain must have an input that maps to it.

Question 10

Injective function

Answer 10

Every element in the domain must map to a singular element in the codomain.
The function must be a one-to-one function.

Question 11

Rule for operations on functions through ordered pairs

Answer 11

When doing operations on functions through ordered pairs, the first element must be the same as the elements must be from the same domain.

Question 12

Sum of a function

Answer 12

(f + g)(x) = f(x) + g(x) for all x in a set

Question 13

Difference of a function

Answer 13

(f - g)(x) = f(x) - g(x) for all x in a set

Question 14

Product of a function

Answer 14

(f * g )(x) = f (x) * g (x), for all x in A

Question 15

Quotient of a function

Answer 15

(f / g )(x) = f (x) / g (x), for all x in A

Question 16

Composite functions

Answer 16

(f ° g)(x) = f( g(x) ), for all x in A

let g: A → B, f: B → C
f ° g: A → C

Question 17

Composite functions domains and codomains

Answer 17

let g: A → B, f: B → C
The domain of f and the codomain of g are both B