Question

How do you find the range of f(x,y)=ln(x+y-3)?

Answer 1

The range depicts all possible values for f(x,y). I can't really tell you the range without knowing the domain.

Answer 2

the domain i got was \[x+y>3\]

Answer 3

The range should be -inf to inf.

Answer 4

how can you tell?

Answer 5

ln of a number between 0 and e gives you a negative number. Between the range e to infinity, it gives you a positive number. etc. Does that help?

Answer 6

Kind of...is there any way to prove this algebraically?

Answer 7

Yes. The limit as x approaches 0 of ln(x) = -infinity. The limit as x approaches 1 of ln(x) is 0. The limit as x approaches infinity of ln(x) is infinity.