Problem

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

01:02

Problem 44 Medium Difficulty

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

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

Answer

$g(x)=\cos x$ and $f(x)=x^{2}$

Discussion

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Video Transcript

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.

Heather Z.

Oregon State University

Topics

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 3

New Functions from Old Functions

Problem