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LiotsCaeitise 96LGiven Ihat { (x) Wa g(x) 2x + find "ch = of the followmns; ' # exists. (fg)(0) (fg) (2) U-m ( - g)(0) Uet (flg)(-V5) (g/f)(-!) Givev that...

Question

LiotsCaeitise 96LGiven Ihat { (x) Wa g(x) 2x + find "ch = of the followmns; ' # exists. (fg)(0) (fg) (2) U-m ( - g)(0) Uet (flg)(-V5) (g/f)(-!) Givev that h( +) and g(x) = Vr- find each of the following: if it exists 12. (gh)(10) 14. (hfg)(1) (hg)( 3) For each pair _ of functions in Exercises 17-34; Find the domain of $, & f + & f - g, fg, ff fl g and g/) Find g) (x) (f - g)(x), (fg)(x) (f)(x) (flg)( x) ,and '(g/f)6x) Me 18. f(x) ~x+ 1, g(x)20. f (*) x + 2, g(x)

Liots Caeitise 96L Given Ihat { (x) Wa g(x) 2x + find "ch = of the followmns; ' # exists. (fg)(0) (fg) (2) U-m ( - g)(0) Uet (flg)(-V5) (g/f)(-!) Givev that h( +) and g(x) = Vr- find each of the following: if it exists 12. (gh)(10) 14. (hfg)(1) (hg)( 3) For each pair _ of functions in Exercises 17-34; Find the domain of $, & f + & f - g, fg, ff fl g and g/) Find g) (x) (f - g)(x), (fg)(x) (f)(x) (flg)( x) ,and '(g/f)6x) Me 18. f(x) ~x+ 1, g(x) 20. f (*) x + 2, g(x)



Answers

For the given functions fand g. find the following. For parts $(a)-(d),$ also find the domain. (a) $(f+g)(x)$ (b) $(f-g)(x)$ (c) $(f \cdot g)(x)$ (d) $\left(\frac{f}{g}\right)(x)$ (e) $(f+g)$ (3) (f) $(f-g)$ (4) (g) $(f \cdot g)$ ( 2 ) $(h)\left(\frac{f}{g}\right)(1)$ $f(x)=2 x+1 ; \quad g(x)=3 x-2$

Going to go in question. We have the function effects. It is to explicitly and function jee ick. But this three x minus two No, The first team which we have to find this f plus de X through the air parties F plus d x. So this is equal to affects plus DX. So we can I reserve the next logics correctness. This is two X plus one left three x mine. Estelle, it is coming as by Rick and this is minus one the parties f minus z x. So this is FX minus. That is we can I just to express well minus three x minus two. So this is where mining to be excellent minus x one and my husband's plus two is last be part is f dot g x. This is effect might have night with DX So this you can directly I just to express mint My dad played it three X minus two under the fighters f delighted by g X. This is equal affects divided by D. X. So that means we can I d says work less one divided by the X minus two. No, you have to find a place G three. So the e parties f blessed e three. So in the political just replacement three. So this is flame like a redwood. Three money. So this is 15 minus one. So that means we can say that 15 miners oneness, flippy f parties f minor full of So in this minor, the extra just a building for listen minus four plus the pathetic will do my Nesler No, next is deep artist F doggy to pull in here will be tested plus one and this is three months of language to minus two finishes would bless one. And this is six minus so four plus one in spite my replacement for So that means this is 20 now the last parties, it's which is have divided by G, the one so here we'll just replacement one for two multiplied with one plus one divided by three multiplied with one minus two. This is coming up two plus one divided by three minus two The desist redivided Bela logistically to be But this is the required

So this problem. We have to find four functions and their domains of plus G minus two f times do enough divided energy. So let's begin by finding f plus g of X. So we're adding together two x squared plus X squared plus one, which is three x squared plus one. So this is our function? Yes. This is a problem. In terms of X, we have no domain. Restrictions are demand is negative. Infinity to infinity. Next, we will do f minus treat. So we're doing two x squared minus the quantity X squared, plus one. And so that gets us X squared minus one as our answer notes and ugly swear. Okay, great. And then again, this is a proble, so we're not going to have any domain restrictions here. So negative. Infinity to infinity. All right. And then you will move on to f times to you the bets. So two X squared Hi ends X squared. This one that gets us to X to the fourth plus two. X squared will be no domain restrictions here. We can take anything we want to the second or fourth powers, so I don't mean this negative. Infinity to infinity and then finally doing F divided by G of X. So we have two x squared over X squared plus one. We have no common factors between the numerator and the denominator here. So we have to leave up into this. And then Jermaine takes another moment of thought because we don't want There's denominator. Two equals zero. However, there's no real number that one squared would get us negative. So there's no issues in the domain. All real numbers will work so negative. Infinity to infinity is our domain. So we've now done all four functions under demeans, so we are done.

Now we're looking at exercise 79 and chapter 36 and one. And we have a Fedex it was two I first three of three x minus two. And do you have x equals four. X Over three. X -2. And we want to add subtract multiply and divide these functions as well as evaluate um those new combination functions. So when we are adding fractions and stuff we want to make sure remember that our domain has to exclude any value that are going to make the Then I mean zero. So after bat we can set three x -2 Equal to zero. And if we saw that we will get um 2/3. So we know that we will need to exclude to third from our domain um throughout most of the problem. And then if they're new fractions, we need to make sure we come back to this and re evaluate what values will make that development area. So for the addition of these two functions we just want to go ahead and write it out when I do use to. Since they have common denominator already this is gonna be super easy because we're just gonna combine like change in the ready. No and keep the denominator the same. So hi dances six my six x minus 3/3 X minus two. And the domain is real. Number six. I stopped. I cannot equal 2/3. Everything else is good. It's just that value. That makes the denominator easier. That's a problem. So now we want to subtract half of X minus DMX. And once again we're gonna combine like terms in the matter. So two x minus four X. Is negative two X. And then we still have that plus through. Keep the drama here is the same. That's the power bi I answered negative two x plus three Over three X -2. And the domain is still access that cannot equal two days. And I'm really sorry about that. That funky looking Adidas and let me go ahead and replace that. Yeah. Yeah. Okay. Now we want to multiplied soup functions together so we want to take it to a first three. Okay. 3 8 -2. Hi. For ex every three months to and here we just want to remember that. And they were so for multiplying and multi podcast. So in the near ready we want to distribute this four X two both terms here. And in the denominator we just want to go ahead and um multiply those together. But I'm actually just gonna leave the genomic uh three x minus two squared. There's no point. And me multiplying it out. It does not add value to the problem. Okay. But when I distribute this four X to the two X plus three I get eight X. Where plus 12 days Over this three X -2 squared. And the domain they still on the move except to every three. All real numbers. Sorry. Exactly. Okay. And now we want to Divide these two functions and because I'm dealing with fractions, I'm actually going to take a moment to write it horizontal instead of as a complex factor. So I can do the division with fraction. We'll see. So you need to change that. It is into multiplication. Okay. And then flip the second factions. Now this is nice because 35 to cancel and we're just like with To a 1st 3 over four X. Yeah. No I do have a modified domain here. I still have that I cannot equal Tuesday but I also now have the X cannot equal zero because that will cause a problem. In my new simplified combined function. They have two values to exclude from the Dummy. Right? And then for E. F. G and H we're going to go ahead and step to those numbers into these functions that was just found. So plus do you have three? It's gonna be six times three -3/3 times three minus two. And that sympathize to three. Then we will have f minus G. F. Four which is gonna be negative two times four plus three Over three times 4 minus two. And this will simplify to negative a half first F. Time G of two. We were plug in two. So we have eight times two squared by 12 time to All over three times 2 -2 Quantity Squares. Which is going to be equal to 7/2. Yes. And then uh sorry I've divided by G. F. one. It's gonna be two time one plus three. Alright, my first I got a little carried away there right over four times one, which is just gonna be five of for us. And those are the answers.

According to good question, we have the function. F X is two weeks early. Be ready by three X minus two on we have the function Do you access for Excavated by two years minus two. Now the first part of the ocean is we have to have these two z x The big toe explicitly could be laggard by three X minus two plus four x divided by three x minus two. So just you have to have the greater part. There's only six expressly divided by three x minus two me bodies f minor Z x. Now this is due, if not three, you're either by three X minus two minus four x divided by create minus two. So this is two x three minor forex. So this is my next to it. Last really ragged, but three x minus two three bodies. You have my reply days too. So this is to express tree might be black, but for its beleaguered by to the X minus two bullets going de parties. We have to do it this to F divided by D X that this is to express three divided by three x minus two fuller delightedly for it. Be worried about three X minus two. The list regulators to expressly the wounded by for it. Now we have to find a bloody three. Well, f bless d honey, simply In addition, functionally replace here three. So this will be six. My divide with three plus three divided by three. Michael played with train minus two. So this is a B plus. Three years 21 9 minus two is seven. So I'm seriously no next to have to find f my energy. So where we have subtracted, there'll be a good place. Four. So this will be minus two. My declared with four plus pretty be wedded by three. Multi. Very good for minus two. So this is coming at minus it. Blustery. This is 12 minus two minus five. Divided by 10 to answer his minus one divided by two. And next we have to find f dot g or affects my plan with X. So this is we have to hear in place off, actually, hair for hair. A light in the multiplication part. You might be glad to left three and for murder. Blagged it, Bill The leg by a three multiplied with toe miners to hold square. So this is four plus 37 My blood with four. My blood with two is eight and this is six minus two. So this is four square. So this is coming. Ask seven my blood with eight. And this is Canada's former bread. For this in this, we can cancer. This is 16 18 19 sixties, two from 37 divided went to and the last bodies. We have to find f divided by G for one. Still, there will just replace with one. Yet despite this will be cool. Blessed three beleaguered by four So five divided by four Done.


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