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Inverse Functions (Intro)

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does mrs. Kilgore and Alfre Annie and we're going to work on some inverse functions today we're actually going to do this in a couple of different lessons just so it won't get so long today we're just going to sort of recognize and talk about what's it mean to be an inverse of the function and look at some grass and and also look at some table and then in the lip play give me what we're going to do is we're going to take a function inside okay if this is the time when was the inverse of this function be friends if you had. After that equals 5 x - 2 what was an inverse that that function look like it wouldn't be 5 x - 2 anymore and then we're also going to check some functions to see if they happen to be inverses of one another and we will more about the domain you may see some problems that might say something like G of X is equal to square root of x - 2 for X is greater than or equal to 0 or something like that don't worry about that in this lesson so much will talk about that next time okay so let's go ahead and just talked to this very briefly here actually about couple thing with Embers had I'm just going to start here with a set of get a focus on their sorry about that are we go I can see that pretty well I hope you you agree there we're going to start with this first question up here and of course we can always have a set of ordered pairs and that's exactly what we have here and we're going to find the inverse that set of ordered pairs now I would probably starts as if I were in the classroom and just ask you hey what's the inverse of that set of ordered pairs might have various ants I guess things that somebody would probably tell me Well the inverse is just going to be those ordered pairs Flip or switch places with the coordinate switch places and that would be exactly right for the inverse of this following that is ticks for one negative five 11 negative 1 700 and -6 chain well there should tell you quite a bit about how we're going to find the inverse of a function okay hook up a little bit farther down here nothing wolf here an inverse of a function is just a reflection across the line f of x equals X let me mention something about a cervix G is it safe to Dexter whatever don't let that notation bother you remember ASA desk and just be re-written as y so we can think of that as why will that so when I come down here and I'll say answer that equals negative 2x + 3 I could just trade places with that asked for that and I could ride it as sometimes that that makes its feel a little better we're more used to that same thing here in my table if I wanted to think of that after that as just why it's just the Y corn and it's just a Haitian we call it now want you to think for just a second and I want you to think back to geometry and the even before that you had this probably in middle school as well but remember we did reflection reflection across one of the things we were reflected across what's the line Y equals at okay and if you'll remember we had some little rules for those an hour rule that if we started with an ordered pair why then to get the point that would be the reflection of that point we just try to places and just like we traded places with that for and that stinks there and made it and I feel that's what we need to think of things are going to trade places here the coordinates are going to try to place it okay so let's take a look and I shall I'm here f of x equals negative Duets + 3 I went ahead and put it in my calculator just to let it help me out here and I just copied some points here and I'll let you double check me on all just make sure I write everything down correctly I pick the meds and then I got some particular wise promise and then I went ahead and I graft those points I just said is this Five Points that I have and what I did hear now let me say something about my grass here this is not a square graph I think it's a play something by 32 or something like that so it's not so you may look at it until why didn't that wife will say it's come up there today to the corner that's but it wasn't at where to begin with that remember if you have the line Y equals at the app that has a slope of 1 and it has a y-intercept 0 and every point so if it's is 1 wives one if X is too wise to if x is negative three wires negative three that's why that grass that line rifle that looks like that it always passes through the origin and it has a slope of 1 now orange here is my graph y equals if 2x + 3 I had asked you for a question over here and I didn't put no one for me I'll get to that in the second we wanted to just grass and we haven't found it yet I'm going to tell you that in the next Lieutenant but let's say that we wanted to grass what's the inverse of this line was well that be easy enough so let's just come back over here and one thing we need to look at it some more notation here if we find COS inverse listen to why we're going to read it but I'll get my hand out of the way and just took that guy if I have F to the negative 1 of it that the inverse of F and that that -1 is not a NetSpend it okay it's just a notation and we read it the inverse all after that we can have the same thing for a gfx or an HVAC store whatever we would just have G to the negative 1 on Snap I'm going to go ahead and I'm going to make a a little table of values here for my inverse as well and I remember I don't I haven't found an equation for it and that's not what I'm interested in right now what would have here if I made a table of values for the inverse all I would have to do is take the table that I have over here and they walk with them that's exactly right I know your son we just need to switch places so my points that would be the reflection of -3 would now be my negative 3 that would be a point on the inverse of that then I'd also have five negative and I'd have three zero and I'd have negative 1/2 and I would have negative 7 and that would 95 points on the inverse of that original function by Mana pulled off to the side they are on I'm going to and I'm going to plot the point 9 negative 3 the double check me here until three four five six seven eight nine and Navy 3 hope that pink will come through sorta thanking the orange kind of look the same and then I'm going to have five- 1 2 3 4 5 and then I have three zero and then I'm going to have negative 1/2 and I have a -7 V 1 2 3 4 5 6 7 and 2 3 4 5 where's my route we're here. There it is and of course I certainly should have a line if I don't have a line I've done something incorrect there I just made a careless mistake something because I had a line to begin with then we're just going to be a reflection the orange and the pink not remember what's going to happen here is if it's a reflection I should be able to just fold across y equals at and every point should land honest reflect hey so let's just take a look there's -3 and then here is Its Reflection Point nine negative 3 now think about it I know that's going to be a little bit hard to see you're going to have to kind of imagine it in your mind I'll try to fold it here just to that but that one's going to land on that okay this point right here is going on. this one this point right here will land on this one this one on this one and this one on this one be patient with me just a moment let's see how close I can come to actually folding that along that thing what what happened how to say yet when you can say maybe one point they are versus versus two points because I have landed on one and have it okay alright everybody sort of clear on at least what an inverse it what what basically we're looking for okay that's one thing you might have to do you may have to actually graph an inverse you may have to look at 1 but looked at just a quick look here and I want to show you some of the types of instruction sometimes I think the instructions are as difficult forces any time I wanted to show you just a couple of things here know this is going to be one exercise that you're going to do and this is the way they asked the instructions did I give you a call option in my FiOS okay it's it's invertible or you can find the inverse of this function now notice on either one of these and basically it's the same same thing here they not giving you a function they've not said f of x is equal to -3x - 7 or anything like that they had just said is invertible and then giving you about five ordered pairs for and the question I've asked you here is okay if it's invertible find F inverse remember this but the little well first thing you not say is oh okay 15 is my exiled over here and not in the Hat's is there now remember we're not ask the 15 where are the spots in value when it's 15 we're finding the inverse of some value after stent what we're going to do if we see F to the negative 1 if it's saying we need to come over here to the y coordinate we need to come over to the eighth of that and then ask Denver's that this thing is going to be 5 because remember when we do teen Converse we trade places with the X and the Y so that 15 becomes they're at and then I walk or not which is what we're looking for for f inverse that the Tang that becomes our pie because we had to quit that older care if we're doing antlers okay does that make sense we got to get in your mind and that will help you as much as anything if I'm doing first I've got to trade places with my coordinates okay I tried twice this with my ex and my wife and that comes from the fact that you can reflect an inverse across like will Caleb see this last one down here then that stuff the function G of X is invertible okay then we're going to find G to the negative 1 of -6 and remember that find the inverse of G find the value of the inverse of G when X is -6 K since I'm doing inverse I'm not going to be here for a -6 ccs y coordinate in their sign agency it's so if I'm dealing for the inverse or looking for the unversed for me bro got a trade places that my ordered pair for the universe will be agonistic play Raz Simone value of the inverse when I used -6 for my  will be zero Hey did that make sense for everyone and like I said I haven't told you yet it's going to be very easy it's not that it's difficult I just don't want you to take up a long long tape here for you and and do did about 40 from exercise cuz I'm a little exercises and that you practice a little bit with this and then on the next video I'll show you how to find an actual inverse Sun from Earth of a given function running over just kind of doing a little in traffic you okay now the last thing I wanted to hear I have chosen straight line here you can have inverses of parabolas or phones or just a curve or Florissant okay I just chose line just because they're kind of easy to get started on an easy forced to sit okay but the concept is the same for whatever the shape happens to be and I will say this and we'll discuss this more on the neck just because you start out with the function that does not necessarily mean that you're inverse will be a function okay so you might start out with a function but you your inverse why not be a sense and we'll talk more about that tomorrow and also how can we figure that out and how can we check that out I'm at The Trestle on here okay I haven't even told you what the fuc nails with the equation is it better you can probably look at it and tell you can get me an equation for and I'm sure but I'm not even interested in that right now okay you're tried to put some very particular I thought we could we could reference those Point okay now I remember this one is lying is represented by at the vet Ranch I have asked you to find F -1 of -5 or the inverse of F at -5 k hearsay at the next so I'm going to go look here to exit -5 1 2 3 4 5 and I'll go down and see what my why I would absolutely free if you had asked you to find f of negative 5 but I didn't ask you to find f of negative 5 did I I asked you to find inverse of -5 F inverse of -5 so if I asked you to find inverse of -5 then that -5 is Ashley going to be my why so I'm going to go over here and I'm going to go to -5 on my why not my ex like I would if it were just at that so I'm going to let that be my wife so I'm going to go. I'm going to start your from the origin I'm going to go down one two three four five and then I'm going to look for the X that goes with that and I'm going to go over once a 3/4 and 8 K so I'm going to have them write me all this point is -5 but my inverse would have the point -5 8K so if you got a grass and your for a if you're asked to find F inverse of a number Dan if it's the inverse of a given number don't count on your ex quotes are your x-axis rather count on your y-axis I went to -5 and then I found out what the ex was it goes with that so that's going to be negative 5 hey which goes right along with the fact that hey this point right here is 8 -5 and remember inverse point we'll just pay the flip is that okay I can do the same time of course you want to look at it and you want to say well what I want to be able to tell exactly what they are so I don't want to have to look at it and say oh that's why 1 7/12 or something like that let's do one more here we found f inverse of -5 what if I asked you to find inverse get one that works here F inverse of negative F inverse of -6 remember our first inclination is to look at it as . what are on the x-axis not if you're doing it has been verse you're going to do more than just say it so you are going to go to your wife and you're going to go down one two three four 56 that I should have been saving account is there let me do that instead so let's do a fan vs. negative Banner so completely that what they would a point on there and I'm going to count down negative said I'm not on my head but because it seems verse I'm going to go down 14567 I think I can I correctly that time so that is going to be a I have not moved right or left any so that's going to be zero and then of course look at what you got your original point on acid Nero -7 your Reflection Point or your point on your inverse will just be the switch if those two that you might say well I'll just I'll just write down whatever that is and then I'll look for -7 and flip it that's exactly right you're looking for if you're doing a inverse of an Amber then you're looking that's the why you're looking for the ad that you need to flip okay alright that make any sense and that's all I'm going to ask you to do on these exercises and then on the next list well actually look at something like maybe like this and say Hey what if you have gionet is 8 equal to negative 3/4 x + 2 What would the end person that be okay. We could get a bunch of points and we could get our new we could grasp Converse pretty easily but maybe we want an actual equation for that and that's what we'll be looking are Netflix and and also showing that some functions are inverses of one another and I have to find them for you tonight and then you'll have two more after that Nashville Lebanon will try to get that done tomorrow okay alright if you need me please contact me by email I think you'll find these two little exercises pretty quick and timer tonight alright holler at me if you need me you all have a good evening bye bye

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Inverse Functions (Intro)

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