Question

Question is in the comments

Answer 1

@mathmale

Answer 2

hint:
as we can see from the definitions, \(f(x)\) is defined at \(x=0\)

Answer 3

how is that?

Answer 4

whereas \(g(x)\) is not defined at \(x=0\)

Answer 5

here is \(f(x)\)

the unfilled circles means that the function is not defined

Answer 6

here is \(g(x)\):