Question

what is the domain of the function y = ln((12 - 4x)/5) five units down. x < 5 x < 3 x < 4 x < 2 - calculus cp ic 25 - 28

Explanation:

Step1: Recall domain of natural - log function

The domain of $y = \ln(u)$ is $u>0$. Here $u=\frac{12 - 4x}{5}$. So we need $\frac{12 - 4x}{5}>0$.

Step2: Solve the inequality

Multiply both sides of $\frac{12 - 4x}{5}>0$ by 5 to get $12 - 4x>0$. Then subtract 12 from both sides: $-4x>- 12$. Divide both sides by - 4 and reverse the inequality sign (since dividing by a negative number), we have $x < 3$.

Answer:

$x<3$