Both functions will be undefined when x = 1.
The denominator of g(x) is undefinded whenever x < 1. therefore, g(x) will be undefined for any x < 1.
In f(x), when both the numerator and the denominator are both negative, the quotient will be positive, therefore, f(x) will be defined. The only time that f(x) will be undefined will be when only one of the numerator/denominator group is negative. So, f(x) will be undefined only in the section -1 < x ≤ 1.
The functions are not equivalent when x ≤ -1; otherwise, they are.