5

Find the Inverse of the function; I(x) (x 5)? _ X 2 5 OAf '(x =Vx + 5, x2 0 ef '(x) = Vx-5 ,x 2 5Ocf '(x)4 5 X< 0None of these...

Question

Find the Inverse of the function; I(x) (x 5)? _ X 2 5 OAf '(x =Vx + 5, x2 0 ef '(x) = Vx-5 ,x 2 5Ocf '(x)4 5 X< 0None of these

Find the Inverse of the function; I(x) (x 5)? _ X 2 5 OAf '(x =Vx + 5, x2 0 ef '(x) = Vx-5 ,x 2 5 Ocf '(x) 4 5 X< 0 None of these



Answers

Find the inverse of the functions.
$f(x)=\frac{5 x+1}{2-5 x}$

All right, So let's do a review question for an versus If I have the function F of ax equals five X over X plus two and we'll set that equal to lie. The typical format is too. Switch your variables and because we know the original function, you input X and output. Why? And on the inverse you'll be in putting why, and out putting X. So we're going to change that to a five y over Y Whoops. Why plus two equals X. And now we need to solve or why. So keep that in mind. You're gonna get all the wise on one side. Now I have to start off by multiplying both sides of the equation by wyffels, too. And then this factor cancels that factor. Now, you might think you like this in factored form, but we actually don't. We want to distribute it now. Remember what we're doing. We're solving for why, so I need to get the y terms together, and I could get this even though it has an ex attached. I need to subtract ex wife on both sides Now. I want to pull out that common factor of why and I have one more step. Dubai those sides by five minus X and I have two X over five, minus fax. And if I want to write that in functional notation, I need know that this is the inverse with the input variable being acts. Can I have two acts over five minus ax?

For this question, we're going to identify the inverse of this function F of X equals five X plus two. First, I'm gonna turn it back into the equation form. By replacing the Vex with white, they get a little bit easier to work with. All right, then we're gonna go ahead and switch around the X and the Y values. So we now get X equals five times. Why? Plus two. And then all we do is simply re isolate the Y value. Some of us attract two from each side continuing this all I'm here. So I have X minus two equals five. Why? And dividing by five on each side. Our final answer is X minus two, divided by five equals. Why or in verse about the bags? Here we go.

For this question, we're going to identify the inverse of dysfunction at the backs equals X minus two, divided by five to start off, we're gonna replace after Becks with why putting it back into the equation form, making it a little bit easier to work with here. Second step is we're going to switch around the X and the Y values, so it should now look like this up here. X equals why minus two Divided by five. All right, now we're gonna re isolate the Wye Valley. First. We need to get rid of this denominator of five. Since this whole expression on top was divided by five, we're gonna multiply by five on each side five times X gives us five acts, and this cross reduces and just leaves us with my Y minus two. And then we're simply going to add Thio. Each side giving us our answer of five X plus two equals y. Now, this is the inverse in equation for, but we can put it back into function notation. The embers of F backs is five x lost too

In this problem were given the 1 to 1 function f of X, and we are asked to find the inverse. You know what is to do this? We're going to take the first step of switching X and Y. You might be looking at this problem saying, there's no why, but I'd like to remind you first that F of X is the same thing, is why? So I'm going to take the X and the Y and swap their spots. So this now reads as X equals two fits times y plus one. Our second step is to resolve for why, in other words, we need to get the white term alone. So this 2/5 sets attached to the Y is going to stay for just a second, and we're going to instead subtract the one that's hanging out by addition. So now X minus one is equal to 2/5 times. Why? Sometimes I like to throw that little multiplication symbol in there because it helps me remember the process for undoing that multiplication. You can do this in one of two ways. I think the simplest option is to undo this division of five Soto undo division of five. We multiply by five on both sides. So this five will be eventually distributed into the parentheses of that binomial turn X minus one. So on the left side, we have five prince sees X minus one equals two times Why again This dot here means multiplication. It's not required of you, but it does show or does indicate to your brain what you should do to undo it. To get this. Why alone? You should undo multiplication by division. So you could do one large division over here where I'm going to encourage you to do a smaller division to the coefficient of five. So the two is on the right side. Cancel. And now we have why equals 5/2 times X minus one. The quantity. So our third and final step is to rewrite as f inverse of X. So I'm gonna take this work over here. And so now I have f inverse of acts is equal to 5/2 times the quantity X minus one. So that's one way to write your answer. But you might notice that there's ah different way you could write it by distributing this five halves into the parentheses, so your second answer could look instead like F inverse of X equals five halves X minus five halves because five halves times negative one gives you that minus five halves, so either answer is acceptable.


Similar Solved Questions

5 answers
288 Part Interpretalion It boints | 289 290 Express in words the meaning the conf , dence intervaSeD4| Iengthalpha291 292
288 Part Interpretalion It boints | 289 290 Express in words the meaning the conf , dence interva SeD4| Iength alpha 291 292...
5 answers
:8- 1 Ii 68 2 2 2DDran;
:8- 1 Ii 68 2 2 2 DDran;...
5 answers
The catenary Xlog {s + 1 V(c? +s2)
The catenary X log {s + 1 V(c? +s2)...
5 answers
Very Iong L-93m concentric cylndrica e $ Dene2n{neaneJimanocztnLorctn C73ieesSncanCneneelecticiaoE = ~2k QKhere Q-O,6UC datermlne the pctentlal oifference betk ean tha shells Viblviala? Express /or ansy @f Unts ofVolt Ufine zero decimal places Please Horget rhlenu Jen M Yout _ Antg negjinve. Tate thc volua Coulomo (On tjnt j8 14-9.'09 Nml/c? Mint here thg Unit Veg*or radidlly qutward
very Iong L-93m concentric cylndrica e $ Dene2n{neane Jimano cztnLorctn C73iees Sncan Cneneelecticiao E = ~2k Q Khere Q-O,6UC datermlne the pctentlal oifference betk ean tha shells Viblviala? Express /or ansy @f Unts ofVolt Ufine zero decimal places Please Horget rhlenu Jen M Yout _ Antg negjinve. ...
5 answers
To determine boiling point of liquids, we need t0 look at both intramolecular and intermolecular forces of attractionName the intra- and inter-molecular forces in the following liquids MOLECULE INTRA-MOLECULAR INTER-MOLECULAR FORCES FORCES Trichloromethane, CHCI Ethanol_CHCCHOH Water; HzOArrange the above compounds in the order of INCREASING boiling points. Justify your answer.
To determine boiling point of liquids, we need t0 look at both intramolecular and intermolecular forces of attraction Name the intra- and inter-molecular forces in the following liquids MOLECULE INTRA-MOLECULAR INTER-MOLECULAR FORCES FORCES Trichloromethane, CHCI Ethanol_CHCCHOH Water; HzO Arrange t...
5 answers
If you buy a bag of potatoes and leave them in a dark cupboard for too long, they will begin to form long white sprouts with tiny leaves. Name this process and explain why the potatoes are behaving as they are.
If you buy a bag of potatoes and leave them in a dark cupboard for too long, they will begin to form long white sprouts with tiny leaves. Name this process and explain why the potatoes are behaving as they are....
5 answers
CAN YOU WRITE LEGIBLY AND CIRCLE THE ANSWERS
CAN YOU WRITE LEGIBLY AND CIRCLE THE ANSWERS...
1 answers
Calculating Future Value. You can purchase a service contract for all of your major appliances for $\$ 180$ a year. If the appliances are expected to last for 10 years and you earn 5 percent on your savings, what would be the future value of the amount you will pay for the service contract? (Obj. 1)
Calculating Future Value. You can purchase a service contract for all of your major appliances for $\$ 180$ a year. If the appliances are expected to last for 10 years and you earn 5 percent on your savings, what would be the future value of the amount you will pay for the service contract? (Obj. 1)...
5 answers
DETAILSCHENEYLINALG2 1.1.001_Solve this system of equations and verify your answer; (If the system is inconsistent enter INCONSISTENT:)2x2 3x3 X2 3x3-15XiXz X3) =
DETAILS CHENEYLINALG2 1.1.001_ Solve this system of equations and verify your answer; (If the system is inconsistent enter INCONSISTENT:) 2x2 3x3 X2 3x3 -15 XiXz X3) =...
3 answers
The following graph is bipartite:True False
The following graph is bipartite: True False...
1 answers
Determine the field lines of the given polar vector fields. $$\mathbf{F}=\hat{\mathbf{r}}+\theta \hat{\boldsymbol{\theta}}$$
Determine the field lines of the given polar vector fields. $$\mathbf{F}=\hat{\mathbf{r}}+\theta \hat{\boldsymbol{\theta}}$$...
5 answers
(0*+) Julod a4} inoqe 6081 j0 Uovejol euibuuo a41 Inoqe .081 J0 uoneIoX Biv =* auil 841 JaAO uolioaljal esixe-X a4} JB4O uolpallal eillasl! Ojuo abueppaj 04} deu Iou pInom uoleuoiSuEJ YpI4M
(0*+) Julod a4} inoqe 6081 j0 Uovejol e uibuuo a41 Inoqe .081 J0 uoneIoX Bi v =* auil 841 JaAO uolioaljal e sixe-X a4} JB4O uolpallal e illasl! Ojuo abueppaj 04} deu Iou pInom uoleuoiSuEJ YpI4M...
5 answers
Derive the equation of total energy conservationin magnetohydrodynamics.
Derive the equation of total energy conservation in magnetohydrodynamics....
3 answers
The mean number of classes taken by 25 students at a certain college is 3 and the standard deviation is 1. what is the margin of error for the 95% confidence interval for the mean? (round to the nearest hundreth)a. 1.23b. 0.39c. 1.18d. 0.12
The mean number of classes taken by 25 students at a certain college is 3 and the standard deviation is 1. what is the margin of error for the 95% confidence interval for the mean? (round to the nearest hundreth)a. 1.23b. 0.39c. 1.18d. 0.12...
5 answers
26_Washing soda (Na COsxnH,O) consists of 63 weight percent of water: How many moles of water (n) per mole of sodium carbonate are crystallized within the structure of washing soda? A 20 8
26_ Washing soda (Na COsxnH,O) consists of 63 weight percent of water: How many moles of water (n) per mole of sodium carbonate are crystallized within the structure of washing soda? A 20 8...
5 answers
Give a limit expression that describes the left end behavior of the function.42x 3x2 f(x) = 19x 2xlim flx) = X7 C(Simplify your answer:)
Give a limit expression that describes the left end behavior of the function. 42x 3x2 f(x) = 19x 2x lim flx) = X7 C (Simplify your answer:)...

-- 0.018152--