Math Problem Statement
Find the domain of the function f(x) = log(x - 16). Write your answer using interval notation.
Solution
To find the domain of the function , we need to identify where the argument inside the logarithm is positive.
For the logarithmic function to be defined, the expression inside the logarithm must be greater than 0:
Solving this inequality:
Thus, the domain of the function is all values greater than 16. In interval notation, this is written as:
Would you like further details on this solution or have any additional questions?
Here are some related questions to explore:
- What is the domain of ?
- How does the base of the logarithm affect the domain of a function?
- What happens to the graph of as approaches 16 from the right?
- Can the logarithm function ever be negative?
- How do you find the domain of a composition of functions involving logarithms?
Tip: Always remember that the argument of a logarithmic function must be strictly positive.
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Math Problem Analysis
Mathematical Concepts
Algebra
Logarithmic Functions
Formulas
Logarithmic Function Domain: log_b(x) is defined for x > 0
Theorems
Domain of Logarithmic Functions
Suitable Grade Level
Grades 9-12