Here are the essential concepts you must grasp in order to answer the question correctly.
Natural Logarithm Function
The natural logarithm function, denoted as ln(x), is the logarithm to the base e, where e is approximately 2.71828. It is defined for positive real numbers and is the inverse of the exponential function e^x. Understanding this function is crucial for determining its domain and range.
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Domain of a Function
The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. For the natural logarithm function ln(x), the domain is limited to positive real numbers, meaning x must be greater than zero, as ln(x) is undefined for x ≤ 0.
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Range of a Function
The range of a function is the set of all possible output values (y-values) that the function can produce. For the natural logarithm function ln(x), the range is all real numbers, as ln(x) can take any value from negative infinity to positive infinity as x approaches zero from the right and increases without bound.
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