SOLUTION: x ∈ ℝ, y ∈ ℝ and the absolute value of x + the absolute value of y = 2. What is the Domain? Previously, I had the domain as all real numbers, but it wa

Algebra ->  Functions -> SOLUTION: x ∈ ℝ, y ∈ ℝ and the absolute value of x + the absolute value of y = 2. What is the Domain? Previously, I had the domain as all real numbers, but it wa      Log On


   

Question 1127040: x ∈ ℝ, y ∈ ℝ and the absolute value of x + the absolute value of y = 2.
What is the Domain?
Previously, I had the domain as all real numbers, but it wasn't right. I'm not sure how to figure out the domain.
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
if x ∈ ℝ, y ∈ ℝ and
abs%28x%29%2Babs%28y%29=2
Domain: R%5E2

Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


I don't think the other tutor understood the problem....

The domain is the set of allowable values for x. You said you had the domain as all real numbers. So look at the equation if x is 5:

abs%28x%29%2Babs%28y%29+=+2
abs%285%29%2Babs%28y%29+=+2
5%2Babs%28y%29+=+2
abs%28y%29+=+-3

An absolute value is always 0 or positive; it can't be -3.

It should be easy to see that we have exactly the same problem if x is -5.

So now can you see what the smallest and largest allowable values are for x?

Those define the domain of your equation.