Question

Determine the domain of the function (f of g)(x) where f(x)=1/ x+3, g(x) =2/x.

Answer 1

(-infinity, -2/3)u(-2/3,0)u(0, infinity)

Explanation:

since it is asking for f(g(x)) we plug g into x which looks like:

f(2/x)

now we plug that into the f(x) equation for all of the x's because that is what replaced the x so:

1/(2/x)+3

we look at the denominator so we can pull the 2/x+3 out and set it equal to zero, therefore solving for x

this gives us -2/3

and we get the 0 from g(x) 's denominator

that should be correct and hope this helps!