Questions: Find the domain of y = log(6-2x).

Find the domain of y = log(6-2x).
Transcript text: Find the domain of $y=\log (6-2 x)$.
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the Argument

The argument of the logarithm is given by \(ax + b\).

Step 2: Determine the Constraint

For the logarithm to be defined, its argument must be greater than zero: \(ax + b > 0\).

Step 3: Solve the Inequality

Given that \(a = -2\) and \(b = 6\), we solve the inequality \(ax + b > 0\). Since \(a < 0\), the solution to the inequality is \(x < -\frac{6}{-2}\). This simplifies to ax + b > 0 \Rightarrow x < -\frac{6}{-2}.

Step 4: Express the Domain

The domain of \(y = \log(ax + b)\) is given by the solution to the inequality, which is x < 3 in interval notation.

Final Answer:

The domain of the function \(y = \log(ax + b)\) is x < 3, where \(a = -2\) and \(b = 6\).

Was this solution helpful?
failed
Unhelpful
failed
Helpful