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Find $ f \circ g \circ h $.

$ f(x) = 3x -2 $ , $ g(x) = \sin x $ , $ h(x) = x^2 $

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$$(f \circ g \circ h)(x)=f(g(h(x)))=f\left(g\left(x^{2}\right)\right)=f\left(\sin \left(x^{2}\right)\right)=3 \sin \left(x^{2}\right)-2$$

01:25

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

Oregon State University

Harvey Mudd College

Idaho State University

Boston College

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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Let $f(x)=\sin (x), g(x)=x…

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$\text { Find } f \circ g …

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Find $f \circ g \circ h$

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we have functions F, g and H, and we're going to find f of g of h. Another way to write that is f of G of h of X like this. So that shows that we're going to have a chav X as the inside function on its going inside G. So we're taking X squared and we're substituting it in for X in the G function, So g of h of X is sign of X squared. That whole thing is going into the F function. So we're taking the sign of X squared and we're substituting it in for X in the F function, and that's going to give us three times the quantity sign of X squared minus two.

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