Functions

Question 1

What is a function?

Answer 1

mapping from x to one element y

Question 2

what is domain and codomain?
What is an image and pre-image?

Answer 2

Domain think “input type”. The Pre-image.
Codomain thnk “return type”. the image.

Question 3

when are two functions equal?

Answer 3

Question 4

equal functions does not depend on equal implementations

Answer 4

Question 5

what is “onto”

Answer 5

Surjection - for all Y, there is an X

All images have a pre-image

Question 6

what is one-to-one or injective?

Answer 6

different elements of the domain map to different elements of codomain

horizontal line test: only one point

Question 7

what is bijective? or one-to-one correspondence?

Answer 7

both one-to-one and onto

every y E Y is th eimage of exactly one x E X

Question 8

Answer 8

-1 is part of codomain that has no preimage

f(-1) = f(1) = 1

Question 9

what is inverse: F-1(x)

Answer 9

maps image to pre-image

Question 10

Cardinality of sets (number of elements)

Answer 10