Thread: Domains

Identify the domain, range, and a possible codomain

1) (x,y) belong to RxR, y=((x^2)-4)/(x-2)

2) (x,y) belong to ZxZ, y=((x^2)-4)/(x-2)

I don't quite understand the difference here.............

Originally Posted by zhupolongjoe

Identify the domain, range, and a possible codomain

1) (x,y) belong to RxR, y=((x^2)-4)/(x-2)

2) (x,y) belong to ZxZ, y=((x^2)-4)/(x-2)

I don't quite understand the difference here.............

If you simplify both of them you get

and the function is undefined if x=2

Now the question you need to ask yourself is What am I allowed to put in for x and y? in the first we are using the set of Real numbers.

As for the 2nd we are only using integers.

So if we only put integers in the 2nd what will come out....

Think on this and good luck.

I guess for reals:

domain: all reals x except x=2
range: the reals
codomain: same as range

For integers:

domain: all integers x except x=2
range: the integers
codomain: same as range

Is this right?

The only way you can obatin y = 4 in your range would be if x = 2 but we know so knowing that what is the range?

Good call, so the range for both problems would exclude y=4, is the answer correct now?

yep you're all set from there.