Homework Sourse1 Select the statement that is FALSE about the function fx y
1. Select the statement that is FALSE about the function f(x, y) = ln(x + y-1).
(A) f(e, 1) = 1
(B) f(4x, x + 1) = ln(5x)
(C) The domain is everything in R^2 except the point (1,0).
(D) The range is all real numbers
(A) f(e, 1) = 1
(B) f(4x, x + 1) = ln(5x)
(C) The domain is everything in R^2 except the point (1,0).
(D) The range is all real numbers
Solution
The statement (C) is false. This is because ln(x+y-1) becomes undefined when (x+y-1)=0. Thus for all points lying on the straight line x+y=1, the function becomes undefined. (1,0) is just one of those points out of an infinite number of points which satisfy x+y=1, hence the statement is false
