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If $ f(x) = x + 4 $ and $ h(x) = 4x - 1 $, find a function $ g $ such that $ g \circ f = h $.
$g(x)=4 x-17$
02:50
Jeffrey P.
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
Missouri State University
Harvey Mudd College
Baylor University
University of Nottingham
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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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