Question

what is the domain of the function (y = lnleft(\frac{-x+3}{2}
ight))?

(x < 2)
(x > 2)
(x < 3)
(x > 3)

Explanation:

⚡ Using what you learned: Identifying Restrictions and Asymptotes

Step 1: Set up the inequality

For a logarithmic function \( y = \ln(u) \) to be defined, its argument must be strictly greater than zero:

$$ \frac{-x + 3}{2} > 0 $$

Step 2: Solve for x

Multiply both sides by \( 2 \):

$$ -x + 3 > 0 $$

Subtract \( 3 \) from both sides:

$$ -x > -3 $$

Divide by \( -1 \) and reverse the inequality sign:

$$ x < 3 $$

Answer:

\( x < 3 \)