for-the-functions-f-and-g-find-a-fgx-b-f-gx-c-f-cdot-gx-and-d-leftfracfgrightx-fxx-7-gx2-x1

Question

For the functions $f$ and $g,$ find $a .(f+g)(x), b .(f-g)(x)$ c. $(f \cdot g)(x),$ and $d .\left(\frac{f}{g}\right)(x) .$ 
$$
f(x)=x-7, g(x)=2 x+1
$$

Charles Carter · Accepted Answer

I love eggs is X 27 and G of X is to explosive one. We were asked to perform several several. Ah, um function operations, I guess, is the best word s o. Here we go. So for part A, we&#x27;ve had to add the two functions. So we add the two functions just combining, like terms. So X and two eggs, I would just be three eggs. So is the some function, and negative seven plus one is just minus six. Thank you for part B. We&#x27;re doing the difference function. So it&#x27;s gonna be f of X minus G of X, so X minus two exes. Negative acts negative. Seven minus one is negative. Eight again. Just combining, like terms for part C. I we&#x27;re doing the product. Okay, so we&#x27;re gonna do some district distributing s so we&#x27;re going to x Times two x, which is two x squared x times one is just plus X negative seven times two exes, minus 14 axe and then negative seven times one is 97 and then combining those two ex terms in the middle will have two X squared minus 13 x 97 and then for party we&#x27;re dividing. Um, so we&#x27;re just gonna just write this as a cl ocean? So we&#x27;re gonna have X minus seven over two X plus one has only function. Okay, Thank you very much.

Charles Carter · Answer

all rights has expired. Minus two. We&#x27;re giving G of axe has three X and were just told to perform the four basic operations. So for a we&#x27;re just finding the sum of f of x and G of X that we don&#x27;t have to combine any light terms. Just put them together. So x squared plus three X minus two for part being were subtracting the same thing. There were no no terms to combine. So line changes that G of X is now negative. Three eggs. When we combine the light terms sees our products. I&#x27;m gonna multiply three x by X squared minus twos. That&#x27;s gonna be three X cubed, minus six x And for part, Dean, we just fine. We just write down the question. Let&#x27;s have X squared minus two. Cover three X. Okay. That&#x27;d be it. Thank you very much.

Wesley Hines · Answer

So we&#x27;re given that f of X is equal to one over X plus street and that G of X is equal to negative two over X arounds to find f of G g of F f F and G M G. So for F of G, we plug e and F, or that is the same as one over negative two over X plus three for GFF Blood F into G or negative to over one over X plus three for F of f. We plug F back into F, which is one over one over X plus three plus three. And for GMG, we plug G back in a G, which is negative two over naked of two over X. So now for F of G, we have to multiply everything by X to get rid of the X in the bottom. This will get X over negative two plus three x, which is acceptable for GFF. We have to multiply everything by experts. Three. This will give negative two X minus six over one, which is equal to negative two X minus six. I will just erase the over one for f of f leave. Most fly by experts. Three. Is this going to be X plus three over one plus three experts nine, which is equal to X plus three over three experts tent and then for GMG. We multiply by X and we get negative two x over naked too, which is equal to x.

Wesley Hines · Answer

were given that F of X is equal to three x plus one, and that G of X is equal to X squared and rest. To find f of g of f f of f N G of G for F G, we&#x27;re going to plug N G into X. That&#x27;s going to be three of X squared, plus one for GFF were going to plug effigies That&#x27;s going to be three x plus one squared for F of F, throwing a blood F into F size, going to be three of three X plus one plus one. And for GMG, we&#x27;re going to plug G into Jeez, that&#x27;s going to be X squared squared for F of G. I was going to be equal to three x squared plus one for G F F three X plus one squared. Well, that is going to be the same as foiling this, but you can also just keep this is three X plus one squared. We&#x27;ll file it very quickly. Just do you get a simple white must be equal to nine X squared plus six x plus one for F of F that&#x27;s going to be equal to nine x plus four. And for GMG that&#x27;s needed equal to X. The fourth

Wesley Hines · Answer

so we&#x27;re given that of X is equal to three over X minus one and that G of X is equal to two over X and rest Defying f of G g of F, F, F and G of G. So for F G, we take G and plug it into EFS. That&#x27;s gonna be 3/2 over X minus one for GFF. We take f and plug it into Jeez, that&#x27;s going to be to over three over X minus one for f of f. We pluck f back into f. So this is going to be three over three over X minus one minus one. And for GMG, we plug G back into G. Then this is going to be too over two over X. So for Africa, we have to multiply everything by X to get rid of the X in the bottom that will be equal to three X over two minus x for gff. Same thing. But we&#x27;ve multiplied by X minus one. So we have to x minus 2/3 for half of F. We have to multiply everything by X minus one style be three x minus three over three minus one times X minus one, which is going to be minus X plus one, which is the same as saying for minus X and for GMG to over two over X. We multiply everything by X and I would be equal to just x because the twos will cancel So f g is three x over to my sex GF is to exercise to over three. FFs is three x minus 3/4 minus x and JIA of G is x.

Caleb Wood · Answer

this problem. We have two functions and the VAX equals X plus seven in the G of X equals one over X squared. So, in part A, we need to find the value of the function f composed of to of one, in other words, is equals f on the outside of G of one on the inside, where the output from g of one we call the input into the function f This equals half of g of one. Do you have one being one? Hopes were right. Then read Fergie. One divided by one squared it&#x27;s and putting one in forex Z equals F off one divided by one squared is one half of one when you put one into f of X. So this equals one plus seven which equals eight. It is the value FF composed of g of one. It&#x27;s gonna part B part B. You need to find the value off the function g composed of F and put if one we can rewrite this to be G on the outside of f of one on the inside of G, this equals G of f of one f of one being in black. One plus seven. Or this becomes G out of value of eight. We put a into G, where these equals one divided by a squared, which equals one divided by eight times A, which is 16 four. So the value 1 64th It&#x27;s a value the function G composed of death of one. Now let&#x27;s go on to part C. In this problem comes part C. When you find an expression for the function F composed of G of X, this will be an expression not in number. This equals f of Do you have X on the inside. In other words, F of G of X being one divided by X squared. So you substitute expression one over X squared in ffx. So this would equal one divided by X squared and then plus seven. Since F of X is X plus seven, half of one over X squared is one door X squared plus seven as the expression for F composed of G of x. So finally finding expression in Part D, that is the function G composed of F of X, very similar part C. But now the rules air afflict where the function G is on the outside G of the function f of axe on the inside or the input This equals G of f of x f of X being X plus X plus seven or we have one divided by the quantity X plus seven squared. This expression here that&#x27;s boxed is the expression of the function G composed of F of banks.

Problem

For the functions $f$ and $g,$ find $a .(f+g)(x),…

Problem 1 Medium Difficulty

For the functions $f$ and $g,$ find $a .(f+g)(x), b .(f-g)(x)$ c. $(f \cdot g)(x),$ and $d .\left(\frac{f}{g}\right)(x) .$
$$
f(x)=x-7, g(x)=2 x+1
$$

Answer

a. $3 x-6$
b. $-x-8$
c. $2 x^{2}-13 x-7$
d. $\frac{x-7}{2 x+1},$ where $x \neq-\frac{1}{2}$

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Elayn Martin-Gay

Beginning and Intermediate Algebra

Catherine R.

Heather Z.

Alayna H.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

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a. $3 x-6$b. $-x-8$c. $2 x^{2}-13 x-7$d. $\frac{x-7}{2 x+1},$ where $x \neq-\frac{1}{2}$

Beginning and Intermediate Algebra

Grace H.

Anna Marie V.

Heather Z.

Caleb E.

Absolute Value - Example 1

Absolute Value - Example 2

Elayn Martin-GayBeginning and Intermediate Algebra

Catherine R.

Heather Z.

Alayna H.

Michael J.

a. $3 x-6$
b. $-x-8$
c. $2 x^{2}-13 x-7$
d. $\frac{x-7}{2 x+1},$ where $x \neq-\frac{1}{2}$

Elayn Martin-Gay

Beginning and Intermediate Algebra