Question

For each of the following functions check whether they are injective (I), surjective (S), both (B) or none of the above ?

Answer 1

(Note that whether f is injective or surjective can depend on the domain X
and the codomain Y of f .)

Q1. f : {-3,-2,-1,0,1,2,3} --> {0,1,4,9}, f(x) = x^2.

Q2. f : {1,2,3,4} --> {5,6,.....,9}, f(1) = 5, f(2) = 8, f(3) = 6, f(4) = 5.

Q3. f = {(1,5), (2,4), (3,3), (4,6) } ⊆ {1,2,3,4} x {3,4,5,6}

Q4. f = {(3,1), (4,0), (5,1), (6,0), 97,1) } ⊆ {3,4,...,7} x {0,1}

Q5. f : {10,11,......,18} --> {1,2,.....,9}, f(x) = x - 9

Answer 2

first one is surjective for sure, since all of the numbers in the codomain get hit by something in the domain.
not injective because for example \(f(-2)=f(2)\) but \(-2\neq 2\)

Answer 3

ya thats what i thought but am not sure about the others

Answer 4

last one looks to be both

Answer 5

second one is injective but not surjective because some of the codomain elements are not images of domain elements

Answer 6

third one looks to be both

Answer 7

4th is surjective since both 0 and 1 are hit, but not injective because
well because for one thing the domain is larger

Answer 8

thanks very much for your help !!!!