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## Main Question or Discussion Point

Could functions be placed into sets?

Such as

Lets say we have some properties which tie these functions together...

f(x) = ax+b

g(x) = cx+d

h(x) = ex+f

f(x)=g(x)=h(x)

This would be several functions which are also constant. Such as a polynomial.

(ax+b)(cx+d)(ex+f), there are three linnear functions which all equal 0.

Another way which I think would be plausible, though I am not sure...

f(x) = ax + b

g(x) = ax + b+1

h(x) = ax + b+2

Or

f(x) = ax + b

g(x) = ax

h(x) = ax

Or

f(x) = ax + b

g(x) = a(x-1) + b

h(x) = a(x-2) + b

The way I think this would work...

Of a polynomial...

120x

Before anyone gets angry about this question, note I am learning about this on my own, and I really don't like how that was done...But it's just a wild guess...Also, it has been bugging me for a bit so I figured I ought to ask about it before I take it too far...

The only thing that makes me think it is plausible is if every function (or if it is a better description, then equation) is tied with every other equation in some manner.

Here is another example of what I mean...

This function list could be tied by two methods (If methods isn't the right word, please tell me which word is correct). Each function in the list is multiplied by x. The second is that as x increases, the next element is used.

Let the domain be the natural numbers, 1,2,3,,,.

L

L

Again, this is just a curiosity...

Thanks for your help...

Such as

**L**=*f*(x),*g*(x),*h*(x)Lets say we have some properties which tie these functions together...

f(x) = ax+b

g(x) = cx+d

h(x) = ex+f

f(x)=g(x)=h(x)

This would be several functions which are also constant. Such as a polynomial.

(ax+b)(cx+d)(ex+f), there are three linnear functions which all equal 0.

Another way which I think would be plausible, though I am not sure...

f(x) = ax + b

g(x) = ax + b+1

h(x) = ax + b+2

Or

f(x) = ax + b

g(x) = ax

^{2}+ bxh(x) = ax

^{3}+ bx^{2}Or

f(x) = ax + b

g(x) = a(x-1) + b

h(x) = a(x-2) + b

The way I think this would work...

Of a polynomial...

**L**= (3x+4), (5x+7), (8x-2)120x

^{3}+ 298x^{2}+ 142x - 56 = L_{1}^{-1}(x) * L_{2}^{-1}(x) * L_{3}^{-1}(x)Before anyone gets angry about this question, note I am learning about this on my own, and I really don't like how that was done...But it's just a wild guess...Also, it has been bugging me for a bit so I figured I ought to ask about it before I take it too far...

The only thing that makes me think it is plausible is if every function (or if it is a better description, then equation) is tied with every other equation in some manner.

Here is another example of what I mean...

**L**= x-1, x^{2}-x, x^{3}-x^{2},,,This function list could be tied by two methods (If methods isn't the right word, please tell me which word is correct). Each function in the list is multiplied by x. The second is that as x increases, the next element is used.

Let the domain be the natural numbers, 1,2,3,,,.

L

_{x}(x)L

_{2}(2) = 4 - 2 = 2. Since the second element is x^{2}- x.Again, this is just a curiosity...

Thanks for your help...