Preview of Inverse, Exponential, and Logarithmic Functions

This final unit in the study of calculus AB begins with a discussion of inverse functions and the algebraic and geometric relationship between a function f and its inverse f ^-1 . The geometric property of f ^-1 as a reflection of f across the line y = x is used to develop a formula for finding the derivative of f ^-1 from f .

Next is an introduction to the function f (x) = e ^x and its inverse f (x) = ln(x) . After a brief discussion of the properties of these functions, we see that the derivative of f (x) = e ^x is in fact e ^x itself, and that the derivative of f (x) = ln(x) is the function , which is the only power function that could not be integrated by reversing the power rule. The derivatives of e ^x and ln(x) are used to develop methods to differentiate functions where x is in the exponent. Finally, the general form of functions that exhibit exponential growth or decay is presented.