Here are the essential concepts you must grasp in order to answer the question correctly.
Logarithmic Functions
Logarithmic functions, such as f(x) = ln(x), are defined for positive arguments only. This means that the input to the logarithm must be greater than zero. Understanding the properties of logarithms is essential for determining the domain of functions involving them.
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Graphs of Logarithmic Functions
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 logarithmic functions, the domain is restricted to values that make the argument of the logarithm positive, which is crucial for finding valid inputs.
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Domain Restrictions of Composed Functions
Inequalities
To find the domain of the function f(x) = ln((x-2)²), one must solve the inequality (x-2)² > 0. This involves understanding how to manipulate and solve inequalities, as the square of any real number is non-negative, leading to specific conditions for x that must be satisfied.
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