Question
\( 1 \leftarrow \quad \) Find the domain of the function. \[ g(x)=\log _{6}(x+8) \] The domain of \( g \) is \( \square \). (Type your answer in interval notation.)
Ask by Graham Martinez. in Saudi Arabia
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The domain of \( g \) is \( (-8, \infty) \).
Solution
1. For the logarithmic function \( g(x)=\log_{6}(x+8) \), the argument of the logarithm must be positive. This gives us the inequality:
\[
x+8 > 0
\]
2. Solve the inequality:
\[
x > -8
\]
3. In interval notation, the domain of \( g \) is:
\[
(-8, \infty)
\]
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Simplify this solution Extra Insights
To find the domain of the function \( g(x) = \log_6(x+8) \), we need to ensure that the argument of the logarithm is positive. This means that \( x + 8 > 0 \). Solving this inequality, we get \( x > -8 \). Thus, the domain of \( g \) is \( (-8, \infty) \). The domain of \( g \) is \( (-8, \infty) \).
