evaluate-the-given-functions-fx-yx-yx2-y2-text-find-fx-x-fx-0-3

Question

Evaluate the given functions.
$$f(x, y)=x y+x^{2}-y^{2} ; 	ext { find } f(x, x)-f(x, 0)$$

Tyler Moulton · Accepted Answer

uh huh. We want to evaluate the given functions for F of X, Y and Z X Y plus x squared minus Y squared. We want to evaluate F of X x minus F of X zero. This question is testing our ability to work with multiple functions in particular assessing our knowledge of the fact that to solve, we simply use methods identical single variable functions. That is. We simply plug in the indicated variable. So for instance, if we first find F of X X will plug in extra X X or Y, then we&#x27;ll do the same for F of X zero. And then we find the difference. So F of X X is simply X times X plus X squared minus X squared or X squared plus X squared plus X squared X squared. Then F of X zero is X +50 plus X squared by the zero squared or x squared. Again, Thus we see there are two evaluated functions of X X and X zero are both X squared. Therefore, we must have that F of X X and F of X zero. Or rather fFS x minus X x zero is experiments X squared equals zero.

Amy Jiang · Answer

okay, so we would see a railway teach even falling. So here we have to. After all, we have negative, too honest one. So that&#x27;s two times negative. Three. Absolutely all of that. So that&#x27;s two times three, which is six and we have their oldest is 20 minus one. So that&#x27;s equal to zero times absolutely of negative. One resorted to terms of absolute probably at one what it&#x27;s two times one would you tickled to? And here we have 1/2 said it&#x27;s too times the absolute value of 1/2 minus one. So we get two times the absolutely of negative 1/2 so that&#x27;s equal to two times 1/2. But you think what&#x27;s one in an effort to this is two times outside relative to minus one so that you put the two times one which is equal to two and then we have X minus one. So this is two times after value of X plus one minus. One said I give just two times up through the value of X, and then we have X squared plus two that&#x27;s too absolutely of X squared plus two minus one, which is equal to two times absolute value of X squared plus one

Ankit Gupta · Answer

in this question, we have given here a function epics such that X Q plus two X. Okay, So what is giving here is that there is any number excellent. And when we apply any rule on this number X such that X cubed plus two X, then it will give the result as a function f x. Okay, so the function efforts will be called as the value of a function at exit, or you can see that the function off. Okay, Now we have to find out the function and indicated values here. So, first of all, we have to find out the function at X is equal to minus two. That means we have to put X is equal to minus two to find out of a new function at minus two. Okay, so I&#x27;m just putting the value at X is equal to minus two in this given room, or we can see that different functions. Okay, so it will be like this minus two pulled you and go into minus two. That will be equal to the A minus. Cool. And that will be equal. Okay, so this is the required value of the function add X is equal to minus two now coming to the next value in which we have to find out. The value of a function at X is equal to minus one. So we will put X is equal to minus one. In this function like that, minus one hold you and plus doing do minus one. So it didn&#x27;t give that as minus one. Well, you will give The desert is minus one and will be minus two. That music will get the result minus tree. Okay, now coming to the next value that is you. So value a function at X is equal to zero will be equal to zero. You&#x27;ll bless who in 20 Okay, so here it will be equal. Duda, aqua simplification zero. So this is what required The your function of X is equal to zero now coming to the next wedding here we have to find out the function. X X is equal pool one my pool. So people put X is equal to one by doing the function. So it will be as one by two Q And bless doing this one, Lleyton. Okay, Now, after simplification, we can see that if one right two will be equal to as one day eat plus one. Okay. Now, after digging else him and simplifying ate the value of function will be equal to nine by eight. Okay, so we can say that for the different values off Excell we have find out the different values off. The function so far for X is equal to minus two. Now this is four X is equal to minus one. This is for X, equal to zero. And this is for X is equal to one vapor. So this is very quiet answered.

James Kiss · Answer

first up with this function f of X. I&#x27;m gonna find a variety of outputs given different inputs in the 1st 1 In our list is f of negative too. So to find f of negative two, we put negative to infer X. It would be two times the absolute value of negative two minus will one which would be equal to two times the absolute value of negative three. Absolute value of negative three is three. So it&#x27;s two times three or six, so 1/2 of negative two is six. Next up is Afro zero half of zero would be two times the absolute value of zero minus one, which would be equal to two times the absolute value of negative one. The absolute value of negative one is one and two times one is two, so F zero is too. Next up is effort 1/2 for 1/2. It&#x27;s found by plugging 1/2 in for acts, so it&#x27;s two times 1/2 minus one in the absolute value, which would be two times the absolute value of negative 1/2 which would be two times 1/2 which would be one so f of 1/2 is equal to one. That stuff is f of to half of to would be found by putting two in for access to times the asset value of to minus one. That&#x27;s the absolute value. That&#x27;s two times the absolute value of one. The absolute value of one is one and two times one is two. So the, uh so after two is equal to two. Next, we have a, uh, X plus one F uh, X plus one. We put X Plus one in wherever we have X so would be f of X plus one minus one, which plus one minus one is just two times the absolute value of X. And that would be all we could dio. So half of ex Post one is equal to two times the absolute value of acts. In the last one f of expert close to same concept, we&#x27;re going to plug X squared plus two in for X. What&#x27;s two times the absolute value of X squared plus two minus one. We can clean up what&#x27;s inside the absolute value, actually, and that will be all we can do. So two times the absolute value of X squared plus one is what we get when we do of X squared plus two

Amy Jiang · Answer

Okay, so we want to run with the ball in function with the indicated values. Here we have. Accident was his own. So this is zero squared, plus two times roll. So that&#x27;s equal to their all. And in here we have excessive with three. So that&#x27;s three squared two times three So magical, denying and plus six, which is equal to 15. And now we have evaluated at negative. You said it&#x27;s negative. Three squared was two times negative. Three. So this is it was nine minus six, which is equal to three. And then we have every base that&#x27;s a squared, plus two times a and then we have negative X. Where did close two times later back. Well, negative. X squared is always positive, so we can rewrite this as X squared and we have minus two X. And then we wanted one over a do not equal to one over a depart to plus two times one over a. So that&#x27;s equal to one over a squared plus two over a

Ankit Gupta · Answer

in this question we have given here or function of eggs we just equal to do into models X minus one. Eso lets its execution first on. We have to evaluate the conscience on the indicated values. That means we have to have made the conscience for the different values off X. Okay, now what is actually given here there is Olive. But Axl and we have a price and rules on this number. X is such that of your subjected one song that know much taking morning. My declared written No. Oh, you have to applied this rule for the different values off answer to find out the value of dysfunction are for the different values off expected. So first will start. Oh, from ministry that ways we have to find out the function for excess tickle toe minus two. Now we have to put excess sickle to ministry in dissipation first. So we will put like this to Wyndham in more minus two minus one. So it will give the result as my industry in more and your reasonable more always give the desert as a positive in new. So it will be called Richie. Ok, really only positive in literally. So it will give that is there gas six after simplification. Okay, now corrected the next. When I just know that, Miss, we have to tell me the function, etc. So we&#x27;ll put lexical does you doing equation first? Like this And this work will give desert One that Mr Considered after simplification F zero we could do. Okay, now we have to deal with the function for the X is good for making. So we will put excessive cordovan metro in this equation first Like this. Now, when we&#x27;re two minus one, give desert minus one made do. And after more removing it will be one made. So we can say that after simplification F one by two will be corporal work. Okay, Now coming to the next which is equal to that means we have to evaluate the function it takes its physical do. So it will be like this from equation for us and miss simplify a so its value will be equal. Do do you now coming to the next which is giving us explosive? That is, we have to replace X by X plus one in equation. Flustered. So the occasion first will be like this. X plus one and rain Istvan against the year One woman against alone. I believe the function at explains room will be equal to two weeks after the reward. Now, the last week you, which is given here as X squared, plus true, so value of the function a X squared plus two will be as according to the question for us to into and I&#x27;m replacing X by X Esquire plus two minus one. So this calculation, after removing this morning, will be equal to doing do ex Esqueda best. And this is a required of annual function at X Physical X squared plus two. So from here, you can see that the f I know all that. The news off the function for the differently news off exit The Postman Waas F minus two and this is England was zero. Goldman was if 12 Ford Waas after festivals F X plus one and the sixth was X squared. Plus two d r. Order. Quite answer for this mission.

Problem

Evaluate the given functions. $$f(x, y)=4 x^{2}-x…

Problem 21 Easy Difficulty

Evaluate the given functions.
$$f(x, y)=x y+x^{2}-y^{2} ; \text { find } f(x, x)-f(x, 0)$$

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