We have two functions here, and the result for g/f (x) is:
[tex]g(x)=1,f(x)=x\Rightarrow(\frac{g}{f})(x)=\frac{1}{x}[/tex]
Then, we have that the domain for this function is that for which the function is defined and is real. Then, we have that the function is not defined for x = 0. Therefore, the domain is:
[tex]D\Rightarrow x<0,x>0[/tex]
Or in interval notation:
[tex](-\infty,0)\lor(0,\infty)[/tex]
In other words, the domain of the function is for any value except x = 0, that is:
[tex]x\ne0[/tex]
Therefore, the option is the first one.
