Problem

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

04:42

Problem 64 Hard Difficulty

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

Answer

$g(x)=4 x-17$

More Answers

02:50

Jeffrey P.

Topics

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 3

New Functions from Old Functions

Discussion

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Campbell University

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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

Heather Z.

Oregon State University

Topics

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 3

New Functions from Old Functions

Top Calculus 3 Educators

Anna Marie V.

Campbell University

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Samuel H.

University of Nottingham