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If $ g(x) = 3 + x + e^x $ , find $ g^{-1} (4) $.

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00:38

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

Oregon State University

Harvey Mudd College

University of Nottingham

Idaho State University

Lectures

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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.

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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.

01:19

If $ g(x) = 3 + x + e^x $ …

00:53

If $g(x)=x^{2}+3 x-1,$ fin…

here we have G of X, and we're looking for G Inbursa four. So let's suppose that G Anversa for was X. That means that G of X is for because the inputs and a function are the outputs of the embers and vice versa. So what we're really doing is we're wanting to find out where G of X is equal to four. So four equals three plus X plus e to the X, and we could subtract three from both sides and we get one equals X plus each of the X. Now, we know there's only one number that makes this true. Since this function has an inverse, it must be 1 to 1. And if we just stop and look at it and think about it for a minute, we can solve by inspection. So how are we going to get the number one here? Well, what if X is zero? You know what? Each of the zero is right. Each of the zero is one, and so we would have one equals zero plus one, so that would work. So if X equals zero, we have the solution

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