What is the domain and range of ln(4-x-y)

What are the answers?

I wasn't given any

Ok it is R^2 I believe

Is it right? :)

To find the domain and range of the function ln(4 - x - y), we need to consider any restrictions on the values of x and y that would make the function undefined.

The natural logarithm function, ln(x), is defined only for positive values of x. In this case, we have ln(4 - x - y), so the expression inside the logarithm must be greater than zero:

4 - x - y > 0

To find the domain, we can solve this inequality for x and y:

4 - x - y > 0
-x - y > -4
x + y < 4

The domain is the set of all possible values of x and y that satisfy this inequality. One way to represent the domain is by shading the region below the line x + y = 4.

Now, let's move on to finding the range of the function. The range of ln(4 - x - y) consists of all the values that it can take on as x and y vary over their respective domains. Since ln(4 - x - y) is a logarithmic function, its range is all real numbers.

In summary:
- The domain of ln(4 - x - y) is represented by the shaded region below the line x + y = 4.
- The range of ln(4 - x - y) is all real numbers.