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Lesson 15: Inverse Functions And Logarithms
The document discusses inverse functions, logarithmic functions, and their properties. It defines an inverse function f^-1(x) as satisfying f(f^-1(x)) = x. It also defines the logarithm log_a(x) as the inverse of the exponential function a^x. Key properties of inverse functions and logarithms are outlined, including: the derivative of an inverse function using the inverse function theorem; logarithm rules such as log_a(xy) = log_a(x) + log_a(y); and converting between logarithmic bases using ln(x)/ln(a). Examples of evaluating and graphing inverse functions and logarithms are provided.
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Introduction to inverse functions, their definition, and conditions for invertibility. Includes graphical representation and steps to find inverse functions.
Overview of the derivative of inverse functions and the Inverse Function Theorem with relevant formulas and relationships.
Definition of logarithms as inverses of exponentials and properties of logarithms, including product and quotient rules.
Examples showing how to combine logarithmic expressions into single logarithms, demonstrating the application of logarithmic rules.
Visual representation of logarithmic functions and their behavior in relation to exponential functions.
The change of base formula for logarithms, demonstrating how to convert between different bases.