Final answer:
The domain of g(x)=ln(5-x) is (5, ∞) and the vertical asymptote is x = 5.`
Step-by-step explanation:
The function g(x)=ln(5-x) has a domain of all real numbers except for those values of x where 5-x is less than or equal to zero. Since ln(x) is not defined for x ≤ 0, we need to find the values of x that make 5-x less than or equal to zero. Solving the inequality 5-x ≤ 0, we get x ≥ 5. Therefore, the domain of g(x)=ln(5-x) is (5, ∞).
The vertical asymptote of the function g(x)=ln(5-x) is x = 5. As x approaches 5 from the right side, the value of ln(5-x) becomes arbitrarily large and negative, indicating an asymptote at x = 5.