Answer
The solutions are
a) $g(1,0) = 0.$
b) $g(0,-1) = 0.$
c) $g(0,e) = 1.$
d) $g(1,1) = \ln 2.$
e) $g(e,e/2) = 1+\ln(3/2).$
f) $g(2,5) = \ln7.$
Work Step by Step
We will substitute for $x$ from the first and for $y$ from the second coordinate from the given point into the function $g(x,y)=\ln|x+y|.$
a) $g(1,0) = \ln|1+0|=\ln 1 = 0.$
b) $g(0,-1) = \ln|0-1| = \ln 1 = 0.$
c) $g(0,e) = \ln|0+e| = \ln e = 1.$
d) $g(1,1) = \ln|1+1| = \ln 2.$
e) $g(e,e/2) = \ln|e+e/2| = \ln (3e/2)= \ln e + \ln(3/2) = 1+\ln(3/2).$
f) $g(2,5) = \ln|2+5| = \ln7.$
