operatornamein-19-22-let-mathrmfxx-cdot-find-mathrmfmathrmgx-and-mathrmgmathrmfx-for-each-given-func

Question

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

Finian Lickona · Accepted Answer

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&#x27;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&#x27;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&#x27;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&#x27;s those two different functions evaluated in different

Finian Lickona · Answer

All right. So for this exercise were given the F of X equals the absolute value of X and G of X equals five minus X. Okay. And so were first asked to find f of g of X. So if we plug in G of X, where all the ex terms aren&#x27;t ffx we yet the absolute value of five minus X. If we want to find g of f of X, we get five minus the absolute value of X and these air actually going to be two different graphs because where the absolute value bars are placed. But, yeah, that is those two.

Amy Jiang · Answer

Okay, so we want to rally the polling, so we have competition. This is a composed of G evaluated at two. So we want to start by finding G evaluated at two. So this is equal to minus two plus three. What did you go to? One. So this gives us that we have f evaluated at one. So this is two times one minus three so that you could two to minus three, which is equal to a negative blood.

Amy Jiang · Answer

Okay, so we want to evaluate the pulling. So what year? This is up. Composed of G. Evaluated at negative two. So we want to start by finding G evaluated at negative two. So this is equal to negative. Negative. Too blustery. Tragical to to 1st 3 Just go to file. Okay, so it&#x27;s plug that in. So we have five or F evaluated at five. It is now two times five minus three. What? Article? To 10 minus three, which is equal to seven.

Amy Jiang · Answer

Okay, so we want to evaluate the polling. So here we have composition. So it&#x27;s really this. So we want to start by finding f evaluated at three. So looking at our equation, that&#x27;s going to be two times three minus three. So at six Ministry, which is your good to great. So it&#x27;s forgot in. So we have G evaluated at three. So this is equal to minus three, but three, which is equal to zero.

Problem

$\operatorname{In} 19-22,$ let $\mathrm{f}(x)=|x|…

Problem 19 Easy Difficulty

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

Answer

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

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Catherine R.

Kayleah T.

Maria G.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

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

Algebra 2 and Trigonometry

Catherine R.

Kayleah T.

Maria G.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Catherine R.

Kayleah T.

Maria G.

Kristen K.

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

Ann Xavier Gantert

Algebra 2 and Trigonometry