Answer:
{x∈ℝ,x≠0}
Step-by-step explanation:
to find the inverse domain just make the function inverse first. so the inverse of f(x)=3/(x-2) is:
[tex] f(x) = \frac{3}{x - 2} \\ y = \frac{3}{x - 2} \\ swap \: the \\ \: variables \: :x = \frac{3}{y - 2} \\ then \: solve \:: \\ 3 = x(y - 2) \\ 3 = xy - 2x \\ - xy = - 3 - 2x \\ y = \frac{2x + 3}{x} \\ {f}^{ - 1} (x) = \frac{2x + 3}{3} [/tex]
then find the domain of the inverse function:
[tex] {f}^{ - 1} (x) = \frac{2x + 3}{x} \\ 2x + 3 = {x∈ℝ} \\ x = {x∈ℝ ,x≠0}[/tex]
Then find the intersection of both domains and you'll get {x∈ℝ,x≠0}.
