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$\operatorname{In} 19-22,$ let $\mathrm{f}(x)=|x| \cdot$ Find $\mathrm{f}(\mathrm{g}(x))$ and $\mathrm{g}(\mathrm{f}(x))$ for each given function.$$g(x)=x+3$$

$f(g(x))=|x+3|$$g(f(x))=|x|+3$

Algebra

Chapter 4

RELATIONS AND FUNCTIONS

Section 7

Composition of Functions

An Introduction to Geometry

Functions

Linear Functions

Polynomials

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

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In mathematics, the absolu…

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01:09

$\operatorname{In} 19-22,$…

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Let $f(x)=2 x-3$ and $g(x)…

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For each pair of functions…

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all right. So for this exercise, we are given that f of X equals the absolute value of X and that g of X equals two X, And we are asked to determine f of g of X and G f of X, where we're gonna start with that g of X. So this is pretty straightforward, which is needed plug B G of X value in for all ex terms in the f of X function. So that's just going to be absolute value of two X and now Fergie of F of X. We need to plug in the f of X term wherever next term occurs in the G of X function. So that's just going to be two times the absolute value of X. And interestingly enough, these are going to form the same graph even though they have different placements of the absolute value bar. Yep, that's those two different functions evaluated in different

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