what is the domain of (f/g)(x)?

Question

{x|x>_0}
{x|x>2}
{x|x>-2}
{x|xer}<--

f(x)=|x|-1,g(x)=1/x
What is the domain of (fog)(x)

{x|x=/-1}
{x|x=/0} <---
{x|xer}
{x|x=/-1,x=/1}

This is too hard I can't get it.

Answer 1

f/g = (|x|-1)/(1/x) = x(|x|-1)

It would appear that the domain is all real x, but since g(0) is undefined, we have to exclude x=0.

But x≠0 is not one of the choices. Is there a typo somewhere?

(f◦g)(x) = f(g(x))
f(g) = (|g|-1) = (|1/x|-1)
Again, x≠0, so you are correct.

Answer 2

Thanks again Mr.Steve
Am I correct on the first one?

Answer 3

Did you not read what I wrote?
g(0) is not defined, so f/g cannot be defined there.

But x≠0 is not one of the choices, so something is amiss.