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Express the function in the form $ f \circ g \circ h $.

$ H(x) = \sqrt[8]{2 + \mid x \mid} $

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02:25

Jeffrey Payo

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 3

New Functions from Old Functions

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

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.

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Express the function in th…

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here we see the function capital H of X, and we want to break that down into a composition f of G of h. Another way to write that is with parentheses. F of G of h of x. Okay, so that shows us that H of X is going to be the innermost function. So if we look back at capital age, it looks like absolute value of X could be the innermost function. So let's let little h of X equal the absolute value of X. Now the question is, what is it inside of? Because that has to be inside of G. So let's figure out g of X. If we let g of X equal to plus X, then it looks like a chav X was put in there in the place of X, so that G of h of X would be to plus the absolute value of X. Now. Thirdly, we want to find the outermost function F. So what is surrounding G of h of X? It's being surrounded by the eighth route. So if f of X is the eighth route of X and if we substitute G of h of X into it, then we're substituting two plus absolute value backs into the eighth route and we do get capital age. That's what we were hoping for.

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