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Q2: Evaluate the function at the given values f(xth)_f(x) f(x) = Sx'+X-5 h...

Question

Q2: Evaluate the function at the given values f(xth)_f(x) f(x) = Sx'+X-5 h

Q2: Evaluate the function at the given values f(xth)_f(x) f(x) = Sx'+X-5 h



Answers

Evaluate the function at the indicated values.
$$
\begin{array}{l}{h(t)=t+\frac{1}{t}} \\ {h(1), h(-1), h(2), h\left(\frac{1}{2}\right), h(x), h\left(\frac{1}{x}\right)}\end{array}
$$

In this question we have given here Ah, function in terms off the that this HD is equal d plus one upon thing. Okay, so we have to find out the value of function at the indicated well news here also, first of all we have given here or what is giving you we have given you up number because that t and when we apply some rules on this number t as reciprocal this number that is one might be than adding with the actual no modesty. So we have applied some Bruce on this number as d plus when my t o find out a function which is called F. So the HD Okay, so this function will be as a function and two on p. R begins in their function. It Acti Okay, Now we have to find out the values or function for the different values off me. So first function will be as h minus one. That means off we have to put a is equal to minus one in this equation first. Okay, so when we put these equal to minus one, so it will be like this minus one plus one upon minus one. Okay, so after simplification, we can say that the value of function at you excessive severity is equal to minus one will be equal to minus two. Now, coming to the next one that this edge to So we have to value the value of function actor is equal to two. That means we've been put these equal to do in this equation first. So it will be two. Plus, when my toe back, weeks after simplification, the value of function will be equal toe fiber. Okay, now the next venue we have to take us TZ quinto one, my two. So the value of function at easy quarter when my two will be as one way to plus when we take reciprocal of one by two here, So it will become so it will again give the result as fly by. Okay, now coming to the next one, which is here, X minus one. So we have to put these equal to X minus one. So according to the question first, when deportees equal to X minus one, it will give the desert as X minus one and plus one upon X minus one. Okay, so we can simply fire here after taking an example and calcium so it will be equal. Toe X minus one. Who will square blessed one upon X minus one. Okay, so we can solve in another form as if I have applied the identity as a minus. We will Esquire, so it will be equal toe Xs square minus two eggs plus one and plus one. Okay, so we can see right through this. Do in place off one plus one and in denominator, it will be X minus one. So this is the required function at P is equal to X minus one. And it last we have to put the is equal to one by X. So the value off this function will be as 20 is equal, Cuban by X one upon. Excellent. And when we take reciprocal offal eg one by excess or it will be excellent. OK, so these all other values or function for the different venues off key. That means we can stay back here. Ah, this value is it minus one then it's too. Then we have find out the edge. When they do, Then we have find out H X minus one. Here and at last we have find out, actually by Excellent. Okay, so these are order are quite answer for this question.

Given this function h of tea, you were gonna evaluate this function at a variety of inputs. The first being h of negative one age of negative one could be found by substituting negative one in for tea. So it looked like negative one plus one over negative one, which is negative one plus negative one or negative one minus one, which is negative. Two. So each of negative one he's negative too. Next one is age of to substitute to infer t. So it's two plus 1/2, which is equal to if you're gonna get a common denominator so that you can add them together to is the same thing. That's four hats Eso four has plus 1/2 is equal to five halves, so each of two is five house age of 1/2 would be equal to 1/2 plus 1/1 half, which is equal to 1/2 plus 2 1/1 half assed, too. When you divide by a fraction, multiply by the reciprocal which is to and then we're just like the previous 1 1/2 plus four halves is equal to five house, so h of 1/2 is also five have keep it going. H of X minus one would be X minus one plus one over X minus one. Think of this as to terms you're adding together that need a common denominator as well. The common denominator would be X minus one. This would be X minus one times X minus one over X minus one plus one over X minus one. Can that would simplify two X minus one You can't allow and you get X minus one plus one ex minus one. That's why this is equivalent. In other words, X minus one times X minus one is X minus one squared plus one over our common denominator X minus. One. That is the best way to write a job X minus one. One more H, uh one over X that would be equal to one over X post 1/1 over X. That's the same thing is one over X plus X 1/1 over X is the same as acts because when you divide by a fraction again, you both by by the wrist of Burkholder. Support here is act, so it's one times X, which is X. Now we need to consider a common denominator. Since we have a denominator of acts, the common denominator is X, so it to scale the second term and multiplying it by X over X. Now we have a common denominator of X, and our numerator would be one plus x times x or X squared over our common denominator. X age of one over X is one plus x squared over hex.

In this question we have given here a function edge. Excellent is equal to X Esquire less food and divided by five. Okay, so we have to evaluate the function for the different venues off. Excellent. OK, so what is given that we have given, you know, number excellent. And when we apply any rule on this giving number such that it's quieting the number than adding food. And then who will tell me is divided by five that will give the result as a function ethics. Okay, so we considered a function is a rule according to this concept, and the function is representing by H excellent. So at Texas is healed the function at Xel. Now we have to find out the value or dysfunction for the different values off Excell and of course, twenties to back knees. We have to put X equal to to find out the value of a function that's too. So we will apply this rule to find out of a new phase two by putting excess equal to two. So when report X is equal to do in this function, it will give the result, as you can see here. So it will be equal to four plus school. That is eight. And it will be equal toe eight by five. So this is the required value of each excellent Texas. According Okay, Now, coming to the next value that is minus school. So we have to put X is equal to minus two in the given rule of you can say that in the value of a text here. So when we put X equal to minus two here, so minus two is quiet. Bless who upon fight. Okay, so hence it will be equal. Toe eight by five again. Okay, so this is a required value off at checks at X is equal to minus two. Now we have to find out the value off checks at X is equal to a so we have to put accessible to weigh in dysfunction. And it will be equal to s a square plus food upon. Right. Okay, now what? We have to we have a photo excessive corporal minus X to find her the value off H minus exit. So when people X is equal to minus X in dysfunction like that, minus excellent and then we'll square plus food and divided back for you. So as you know that when father is even, it will give the result in was reform, so H minus exit will be equal to excess. Quiet. Bless who upon five. That means we can say that it would be equal to the value of Egypt. Okay, Now that means function is even the next value, which is given here as a minus two. That means we have to find the value of function at X is equal to a minus. Who? So it wouldn't be as a minus two and hold Squire plus full upon fight. Now we have to simplify them. So I'm just applying the hill that the identity a minus legally square. So it will be as a Squire plus school minus who a and plus who? Okay. So it wouldn't be as a square minus what a and plus a upon fight. So this is the video of the function as a minus two. Okay, now, coming to the next value, we have to find out the value of the function for X is equal to on the road X. Now what do we have to put on the road exit in place off Excell. So when we put under load Excellent in place off. Excellent. So it will be like this You can see here and when we simplify it, so it would give the result as explosive food upon five. Okay, so from l these values we can say that we have find out all the different in function so far that different values off exit. Okay, the first one waas edge to that is here. And the next one was similar. Eight for five and third was etch gauge the next waas EJ minus eggs which is equal to effects here and similarly at a minus two waas equal to this and edged Food X would be equal to this. Okay, so these all are quite answer for this question.

Given the function age. We want to evaluate this function for a variety of inputs. The first being age of two. Define agent to you. Put two in for X two squared plus for over five. Two squared is for so it's four plus four or five or eight fifth So so a trip to is a neat fits. The next one is age of negative, too. Each of negatives You can be found by plugging negative to infer axe, so it's negative two square plus for over five negative. Two Squared is also positive for so it's for post for over five or again 8/5. So h of negative two is also ate fifths. The next one on the list is H A. By an age of a you plug aim for X so it's a squared plus 4/5. There is nothing to simplify here. A squared plus 4/5 is h of a next one is h of negative acts. So we put negative X in for X, but you sit no negative. X squared is negative. Extends negative acts, which is positive X where so age of negative X is expert plus for over five. Each of a minus two each of a minus two would be a minus. Two squared plus four or five now a minus two. Swear careful is not just a square. It was Ford's. Anything being swear. It is defined as multiplied by itself. So it's a minus. Two times a mines to you, plus 4/5. You know you can for you all this out. A squared minus two a minus to a plus four or a squared minus four plus four plus four over five, which is a squared mine for a plus 8/5, that is Age of a minus two. You've got one more H of the spirit bags. Looks word of X in for X, the square root of X Weird is X the square counter axis Where route. So it's experts for over five


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