- #1
Supierreious
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Homework Statement
c) Is 'g' a surjective function (onto) ? Justify your answer.
Homework Equations
Let 'f' be a relation on ℤ (the set of integers) , defined by the entrance requirement :
(x;y) ∊ ƒ iff y = x + 15
and let 'g' be the function on ℤ defined by the entrance requirement :
(x;y) ∊ g iff y = 5x(to the power of 2) + 7
The Attempt at a Solution
The steps I follow is the following :
1. Clarify to myself what surjective is.
2. Confirm the correct function or relation to use, and substitute the x and y with real values.
3. Write out the formula with the proof in the required format.
1 : Surjective :
When we have a function , with a set A and a set B, as example, and all the elements of set B is mapped to an element in A. f: A→B (function f on set A to B), is a surjective function if the range of f is equal to the codomain of f, ie, f[A]=B.
2. The function to use is : (x;y) ∊ g iff y = 5x2 + 7
g(1) = 5(1)2 + 7 = 32
g(2) = 5(2)2 + 7 = 107
g(3) = 5(3)2 + 7 = 232
Rewriting the (x;y) in each of the above examples :
(1;32)
(2;107)
(3;232)
* 3.
This is how far i have gotten. My set 'A' can be defined as {1;2;3} used in my example, but i am not sure what my set B is, and if i am not sure what my set B is , then i cannot really say if every element of my set B can be mapped to set A. Not sure if this makes sense :(