what is the domain of the function $y = lnleft(\frac{-x + 3}{2}\right)$?\n$x<2$\n$x>2$\n$x<3$\n$x>3$

Explanation:

Step1: Recall domain of natural - log function

The domain of $y = \ln(u)$ is $u>0$. Here $u=\frac{-x + 3}{2}$. So we set up the inequality $\frac{-x + 3}{2}>0$.

Step2: Solve the inequality

Multiply both sides of $\frac{-x + 3}{2}>0$ by 2 to get $-x + 3>0$. Then add $x$ to both sides: $3>x$, which can be written as $x < 3$.

Answer:

$x<3$