Define g: Integers to Integers by g(n)=4n-5. Is g injective? surjective? justify your answer
injectivity
suppose g(n)=g(m) for some m element of integers
4n-5=4m-5
4n=4m
n=m
so therefor this statement is injective since each element of g(n goes to an element of g(m)
for surjectivity i know i have to let b E integers and let a E integers since g:integers to integers and i know i have to show that f(a)=b. so:
f(a)=b
4a-5=b
a=
=b+5-5
=b
this is wrong, but i don't understand why. i tried following the books example, but i guess it only works for their specific example.
how am i to show a generic proof for surjectivity in this case? i know that f(a)=2 has no solution in integers (from what my professor wrote on my paper). as well, how do i write the integers symbol using latex?
thank you,
Scott