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Find $ f \circ g \circ h $.

$ f(x) = \mid x - 4 \mid $ , $ g(x) = 2^x $ , $ h(x) = \sqrt{x} $

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$\left|2^{\sqrt{x}}-4\right|$

01:19

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

Campbell University

Baylor University

Idaho State University

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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$\text { Find } f \circ g …

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00:41

here we have functions F, g and H, and we want to find f of g of h. Another way to write that is like this with parentheses, f of G of H and when we write it that way we can see that the inside most function is h of X. So we're going to take a chav X, and we're going to substitute in two G of X, so that gives us G of h of X. So G of h of X is going to be two to the power of square root. X now G of h of X gets substituted in two f of X. So we're going to take that whole thing that we just found and substituted in two F of X, and that's going to give us the absolute value of two to the square root X minus four

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