What is the domain of the function y = ln (-x+3/2)a. x<2b. X>2c. x<3d. x>3

Answer:Option C is correct.x < 3Step-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]orx -3 < 0          [ ∵a > b ⇔ -a < -b ]Add 3 both sides we get;x -3 +3 < 0 +3Simplify:x < 3therefore, the domain for the given function is, x < 3