- #1
Supierreious
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Homework Statement
Determine the dom(g)
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
What i understand from functions :
1. A function is a special type of relation, however, it is a relation
2. A function refers to the ordered pairs, and that every (x;y) will only have the x from the first set once, and also every x from the domain elements.
2. A relation means that 2 sets will be involved.
Having a look at the question :
a) Determine the domain, of the function 'g' : (x;y) ∊ g iff y = 5x(to the power of 2) + 7 :
Dom(g) = {x | for some y ∊ ℤ , (x;y) ∊ function 'g'}
= {x | for some y ∊ ℤ, y = 5x(to the power of 2) + 7
= {x | for some y ∊ ℤ, where y > 0}
= ℤ
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Now here is where i don't know what to do. I can describe what i think the 'Domain' is of function 'g', but other than that I don't know how to say in a formal way what it is ( not quite sure what is required in addition).
I am aware that the Domain elements refer to the 'x' elements. So in a relation, there are 2 sets, and the sets are paired up to form a relation (x;y), and for a function, (x;y) = (x;z) so if x is the same, the second element will be the same ( y=z).
Here 'x' can actually be any ℤ , positive or negative, due to the fact that if it is to the power of 2 , the outcome is anyways positive.
For this reason i cannot pinpoint exactly what the scope of the domain is, because there is no limit, other than being an element of ℤ.
If i am correct in thinking this way, please help me with the correct way to structure my answer, as i would also like to make it easier for me to adapt to the correct custom in formalizing my answer.
Sorry for typing the long essay with so little calculations... :P