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Find a formula for the inverse of the function.

$ f(x) = e^{2x - 1} $

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$y=\frac{1}{2}(1+\ln x) \cdot \operatorname{So} f^{-1}(x)=\frac{1}{2}(1+\ln x)$

01:57

Jeffrey Payo

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 5

Inverse Functions and Logarithms

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Campbell University

University of Michigan - Ann Arbor

Idaho State University

Boston College

Lectures

04:31

A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

12:15

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

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Find the inverse of the fu…

we're going to find the inverse of this function, and the first thing I'd like to do is replace F of X with y So we have y equals e to the two X minus one. Now for the inverse we switch X and y So we get X equals E to the two y minus one. And now we sell for Why? So we're going to need logarithms to undo this exponential function so we can take the natural log of the left and the natural log of the right. We can use the power property to bring the two y minus one down and make it a product instead. So we have natural log of X equals a quantity to why, minus one times a natural law. Gov. And remember, the natural log A B is just one. So we have the natural. Lagerback's equals two y minus one. Let's add one to both sides and we have one plus natural log of X equals two y and then we can divide both sides by 21 plus natural log of X, divided by two equals y. Now let's call that F inverse of X. So f inverse of X is one plus natural log acts over to

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