Bonds from the U.S. Treasury are selling at 102.293, bonds from Alachua County are selling at 85.681, and bonds from the city of
2 answers:
You might be interested in
Answer:
Step-by-step explanation:
As the statement is ‘‘if and only if’’ we need to prove two implications
is surjective implies there exists a function
such that
.
- If there exists a function
Let us start by the first implication.
Our hypothesis is that the function is surjective. From this we know that for every
there exist, at least, one
such that
.
Now, define the sets . Notice that the set
is the pre-image of the element
. Also, from the fact that
is a function we deduce that
, and because
the sets
are no empty.
From each set choose only one element
, and notice that
.
So, we can define the function as
. It is no difficult to conclude that
. With this we have that
, and the prove is complete.
Now, let us prove the second implication.
We have that there exists a function such that
.
Take an element , then
. Now, write
and notice that
. Also, with this we have that
.
So, for every element we have found that an element
(recall that
) such that
, which is equivalent to the fact that
is surjective. Therefore, the prove is complete.
Answer:
y = 2x + 1
Step-by-step explanation:
formula for equation of graph:
substitute m = 2 and c = 1 into the equation