Math Problem Statement
Domain and range
Solution
The given function is:
Domain:
The natural logarithm function, , is only defined when . Therefore, for to be defined, we must have:
Solving this inequality:
Thus, the domain of the function is:
Range:
The range of the natural logarithm function is all real numbers, as it can take any value from to . Since there are no restrictions placed by the function , the range of is:
Summary:
- Domain:
- Range:
Would you like further details on how the logarithmic function behaves or any additional clarifications?
Here are five related questions to expand this topic:
- What is the derivative of ?
- How does shifting the logarithmic function affect its graph?
- Can you calculate the inverse of ?
- What is the behavior of as ?
- How does the range of compare to other logarithmic functions, such as ?
Tip: When determining the domain of logarithmic functions, always ensure the argument inside the logarithm is positive.
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Math Problem Analysis
Mathematical Concepts
Logarithmic Functions
Domain and Range
Formulas
f(x) = ln(x + 1)
Theorems
Logarithmic function properties
Suitable Grade Level
Grades 10-12