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Express the function in the form $ f \circ g $.
$ F(x) = (2x + x^2)^4 $
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01:22
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
Johns Hopkins University
Missouri State University
Campbell University
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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Use the given functions f …
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here we have capital f of X, and we're told to think of capital F of X as the composition F of G and another way to write that is, using parentheses f of G of X that shows us that G is going to be the inside function and f is going to be the outside function. Now there are different ways we could make this work. But the most obvious way is if we let the inside function B two X plus X squared. So we're gonna let G equal two x plus X squared. Now what would the outside function be? Well, what are we doing to that thing? We're raising it to the fourth. We'll just call that thing X. So that means that G of X is two x plus x squared and f of X, his X to the fourth power. And when you put G inside f, you get capital F
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