Question

How to find the domain

Answer 1

We have two functions here, and the result for g/f (x) is:

`g(x)=1,f(x)=x\Rightarrow((g)/(f))(x)=(1)/(x)`

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:

`D\Rightarrow x<0,x>0`

Or in interval notation:

`(-\infty,0)\lor(0,\infty)`

In other words, the domain of the function is for any value except x = 0, that is:

`x\\e0`

Therefore, the option is the first one.