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

$ F(x) = \cos^2 x $

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01:05

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

Campbell University

Oregon State University

Harvey Mudd College

University of Nottingham

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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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here we have capital F of X equals co sine squared X and another way to write that is co sign of X quantity squared. Okay, we're told to think of capital F of X as a composition of F of G and another way to write that is with parentheses f of g of X. If we write it this way, we can see that G of X is the inside function and f of X is the outside function. So looking back at what we were given, Coastline X is the inside function. So let's let g of x equal co sign of X and then the outside function is the squaring function. So let's let f of x equal x squared. And if we were to put co sign of X into f of X, we would get our original capital F function.

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