Answer:
Option C is correct.
x < 3
Step-by-step explanation:
The domain of a function is the set of input or arguments values fpr which the function is real and defined.
For a positive value of logarithmic (ln)
[tex]ln x[/tex] , x > 0.
Given: [tex]y = \ln(\frac{-x+3}{2})[/tex]
⇒ [tex]\frac{-x+3}{2} > 0[/tex]
Multiply both sides by 2 we get;
[tex]-x +3 > 0[/tex]
or
[tex]-(x-3)>0[/tex]
or
x -3 < 0 [ ∵a > b ⇔ -a < -b ]
Add 3 both sides we get;
x -3 +3 < 0 +3
Simplify:
x < 3
therefore, the domain for the given function is, x < 3
