Questions: Find the domain of the logarithmic function and then graph the function. f(x) = ln(-4 - 3x) Find the domain of the function. (Type your answer in interval notation. Use integers or fractions for any numbers in the expression)

$Find the domain of the logarithmic function and then graph the function. f(x) = ln(-4 - 3x) Find the domain of the function. (Type your answer in interval notation. Use integers or fractions for any numbers in the expression)$

Transcript text: college.ec Content / Fall 2024: MATH-13 Do Homework - Section 2.1 E arson.com/Student/PlayerHomework.aspx?homeworkId=686160242\&questionld=5\&flushe M8) 2.1 Enhanced Homework Question 25, 2.1.53 Part 1 of 2 Find the domain of the logarithmic function and then graph the function. \[ f(x)=\ln (-4-3 x) \] Find the domain of the function. $\square$ (Type your answer in interval notation. Use integers or fractions for any numbers in the expres

Solution

Solution Steps

Step 1: Determine the Domain of the Logarithmic Function

The function given is $ f(x) = \ln(-4 - 3x) $. The domain of a logarithmic function $ \ln(u) $ is $ u > 0 $. Therefore, we need to solve the inequality: \[ -4 - 3x > 0 \]

Step 2: Solve the Inequality

To find the domain, solve the inequality: \[ -4 - 3x > 0 \] Add 4 to both sides: \[ -3x > 4 \] Divide both sides by -3, remembering to reverse the inequality sign: \[ x < -\frac{4}{3} \]

Final Answer

The domain of the function in interval notation is: \[ (-\infty, -\frac{4}{3}) \]

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