- #1

Jim01

- 36

- 0

## Homework Statement

Let J

_{3}= {0, 1, 2}, and define functions

*f*and

*g*from J

_{3}to J

_{3}as follows: For all x in J

_{3},

f(x) = (x

^{2}+ x + 1)

*mod*3 and g(x) = (x + 2)

^{2}mod 3.

Does f = g?

## Homework Equations

## The Attempt at a Solution

The above is an example from the book. The section is called Equality of Functions. The procedure is given on how to solve the problem, but no explanation is given for what

*mod*3 means or what it is used for.

Here is the solution:

Yes, the table of values shows that f(x) = g(x) for all x in J

_{3}.

__x__

__x__

^{2}+ x + 1__f(x) = (x__

^{2}+ x + 1)*mod*30 1 1

*mod*3 = 1

1 3 3

*mod*3 = 0

2 7 7

*mod*3 = 1

__(x + 2)__

^{2}__g(x) = (x + 2)__

^{2}4 4

*mod*3 = 1

9 9

*mod*3 = 0

16 16

*mod*3 = 1

I have poured through my elementary algebra, intermediate algebra, pre-calculus and calculus I books and can find no information on equality of functions. Is it called something else by other books? Would someone please explain this to me?

Edit: Sorry for the poor table. While it looks right when I make it, it does not format correctly when I post it.