In the first question f(x) = x + 2/x
f(x) does include 0 in this case if x = i * sqrt2
Therefore f(x) does include all real numbers including 0
x cant be 0 because 2/x yields an undefined result
In the 2nd f(x) = 2/x
x cant be 0 as it would yield an undefined result aswell
f(x) cant be zero but it can get approximately close with x being infinite
I miss the days when I was doing math this easy :) Currently doing control systems specifically bode plots and z transforms.. ugh so boring.
And no you arent being harsh on teachers, alot of them are really unqualified in imparting knowledge on their students. They may know the material but they dont know how to teach, I have come across alot of teachers like that both at school and university. Someday when i leave the private sector I want to go into teaching.
Given the number of errors that the teacher apparently didn't catch, I'd have to disagree with the assertion that this one, at least, may know the material.