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Problem

Suppose $ g $ is an even function and let $ h = f…

04:42

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Problem 64 Hard Difficulty

If $ f(x) = x + 4 $ and $ h(x) = 4x - 1 $, find a function $ g $ such that $ g \circ f = h $.


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02:50

Jeffrey Payo

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Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 3

New Functions from Old Functions

Related Topics

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Integration Techniques

Partial Derivatives

Functions of Several Variables

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Top Calculus 3 Educators
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04:31

Multivariate Functions - Intro

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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12:15

Partial Derivatives - Overview

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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Video Transcript

all right, we have function h of X. And according to the problem, H of X is the composition of G of F. So f is the inside function, and we know that we need to find the outside function and somehow there's a times for involved. So let's do a little bit of playing around with it. So what if g of x waas just for X, what would we get for GFF? We would get four times the quantity X plus four, so that would be four times X plus 16. Well, that's not quite right because we wanted four times X minus one. We have plus 16. So this answer is 17 too large. So what if we then compensated for that by subtracting 17 in our G of X? That would give us for X minus one. So that means that G of X must be for X minus 17 so that we can substitute X plus four into it and end up with age of X

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Calculus: Early Transcendentals

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Related Topics

Functions

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Video Thumbnail

04:31

Multivariate Functions - Intro

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.

Video Thumbnail

12:15

Partial Derivatives - Overview

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.

Join Course
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