how do i know whether the symmetry of g(x)=x/(x-1)^2 is odd, even or none?

Answer 1

See to know the symmetry find out f(x) and f(-x).
If f(x) =f(-x) then its even.
if f(x) = -f(x) then its odd.
owise its none.
Here
f(-x)= -x/(-x-1)^2 = -x/(x+1)^2
f(x) not equal to f(-x) .
hence its none.

Answer 2

None, g(1) is not defined because you have 0 in the denominator when plugging x=1.

g(-1) = -1/(-1 - 1)^2 = -1/(-2)^2 = -1/4