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

$ R(x) = \sqrt{ \sqrt{x} - 1} $

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02:00

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

Baylor University

Idaho State University

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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.

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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 have the function R of X, and we're going to think of it as a composition f of G of h. Another way to write that would be f of G of h of X. So basically, we want to figure out what f g and h r To make this work. H will be the innermost function. And the innermost function we see is the square root of X. So let's let h of x equals the square root of X. Now we need the middle A or G G would be what h of x was plugged into. So if we let g of x b X minus one, we could see that if we were to calculate G of h of X, we would get square root of X minus one. So that's inside the outside radical. So that means the outermost function f is the outside radical. We'll call that square Rydex. So you see, if we were to put G of h of X inside a bath, we would be putting the square root of X minus one inside a square root. And that was our goal. That was what we were trying to get

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