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Learn how to find the formula of the inverse function of a given function. For example, find the inverse of f(x)=3x+2.
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Sal explains what inverse functions are. Then he explains how to algebraically find the inverse of a function and looks at the graphical relationship between inverse functions.
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Let's explore the intriguing relationship between a function and its inverse, focusing on the function f(x)=½x³+3x-4. We delve into the derivative of the inverse of f, applying the chain rule and the power rule to evaluate it at x=-14.
Not all functions have inverses. Those who do are called "invertible." Learn how we can tell whether a function is invertible or not.
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This topic covers: - Evaluating functions - Domain & range of functions - Graphical features of functions - Average rate of change of functions - Function combination and composition - Function transformations (shift, reflect, stretch) - Piecewise functions - Inverse functions - Two-variable functions
Practice evaluating the inverse function of a function that is given either as a formula, or as a graph, or as a table of values.
An exponential function represents the relationship between an input and output, where we use repeated multiplication on an initial value to get the output for any given input. Exponential functions can grow or decay very quickly.