what is the domain of the function y = ln((-x + 3)/2)?\no x < 2\no x > 2\no x < 3\no x > 3

Explanation:

Step1: Recall domain of natural - log.

The argument of the natural - logarithm function (y = \ln(u)) must be (u>0). Here, (u=\frac{-x + 3}{2}), so we need (\frac{-x + 3}{2}>0).

Step2: Solve the inequality.

Multiply both sides of the inequality (\frac{-x + 3}{2}>0) by 2 to get (-x + 3>0).

Step3: Isolate (x).

Add (x) to both sides of (-x + 3>0) to obtain (3>x), which is equivalent to (x < 3).

Answer:

(x<3)