Domain and range of a function of several variables

[yango_17]

Homework Statement

Find the domain and range of the following function:
f(x, y) = ln(x+y)

Homework Equations

The Attempt at a Solution

I know that the natural log ln(x) is only defined when x>0, so does that mean that ln(x+y) is only defined when x+y>0? Also, would the range just be all positive real numbers? Thanks

 

[Mark44]

Homework Statement

Find the domain and range of the following function:
f(x, y) = ln(x+y)

Homework Equations

The Attempt at a Solution

I know that the natural log ln(x) is only defined when x>0, so does that mean that ln(x+y) is only defined when x+y>0?

Yes.
Do you understand what this set looks like in the plane?

Also, would the range just be all positive real numbers? Thanks

No. What's the range of y = ln(x)? Is it just the positive reals?

 

[yango_17]

I don't understand what the set looks like in the plane. The range of ln(x) would be all real numbers, since it has an asymptote at y=0 where is approaches -∞, and approaches ∞ as x approaches ∞.

 

[Mark44]

I don't understand what the set looks like in the plane.

Can you graph the inequality $x + y \ge 0$?
If not, graph the line x + y = 0. The inequality will be one side or the other of that line. Surely you must have done some graphing of inequalities in the past.

 

[yango_17]

I see what you're saying. Regarding the range, however, would it simply be all real numbers due to the range of ln(x) being all real numbers?

 

[Mark44]

I see what you're saying. Regarding the range, however, would it simply be all real numbers due to the range of ln(x) being all real numbers?

Yes.