Question
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Find the domain of the function.
The domain of
(Type your answer in interval notation.)
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Find the domain of the function.
The domain of
(Type your answer in interval notation.)
Ask by Brewer Schneider. in the United States
Mar 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The domain of
Solution
-
For a logarithmic function of the form
, the argument must be positive: -
In the function
, the argument is . Thus, we require: -
Solve the inequality:
-
Therefore, the domain of
in interval notation is:
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Simplify this solution Mind Expander
To find the domain of the function
- Subtract 7 from both sides:
.
This means the function is defined for all values greater than -7. In interval notation, the domain of
To clarify how logarithmic functions work, it’s vital to remember that the input (the argument) must always be greater than zero. If we try to plug in a value that makes the argument negative or zero, we’ll be left with an undefined function. So as a quick tip, always check the condition of the argument when dealing with logarithmic functions!
