The domain and range of ln(4-x-y).

Thanks.

hello there, this what I've get

Df = { (x,y) / x+y =/= 4 }

Range of f is: (0,+infity)

ops is not correct

To determine the domain and range of ln(4-x-y), we need to consider two things: the domain and the range of the natural logarithm function.

1. Domain:
The natural logarithm function ln(x) is only defined for positive real numbers. Therefore, we need to find the values of (4-x-y) that make it positive.
Solving for (4-x-y) > 0:
4 - x - y > 0
-x - y > -4
x + y < 4
In other words, the domain of ln(4-x-y) is all the points (x, y) that satisfy the inequality x + y < 4. This forms a region in the xy-plane.

2. Range:
The range of the natural logarithm function ln(x) is (-∞, +∞), which means it can take any real number as its output.
Therefore, the range of ln(4-x-y) is (-∞, +∞).

In summary:
Domain: The set of all points (x, y) that satisfy the inequality x + y < 4.
Range: (-∞, +∞).