Videos

Composition of Functions

Added Apr 20, 2020 •

Copy this URL:
Embed code:	<iframe class="edlio-embed-player" type="text/html" width="640" height="360" src="//www.bvps.org/apps/embed/?v=256027" frameborder="0" allowfullscreen></iframe> Change dimensions

Show Transcript

hi folks it's mrs. Kilgore and I was praying and we're going to do work on some algebra today we are changing gears just a little bit we might still have some some radicals can certain places that but we're off to just the simplifying radicals now we want to go on to something called composition of function and I hope this finds everybody well and and doing well I heard some of you and that's always good for me bro if you need me please reach out to me by email and I will get back to you just as soon as possible I have had the one person to take me up on my Challenge in a cup the last time I asked that was Tiffany ace and I appreciate her doing that problem for men and she got a little prize and I hope she's stated in the mail by now there might be some more challenges along the way as we get in okay that we're dealing here with composition of functions I think you'll like this it's very it seems to be very straightforward demand and there's a process can you do it and basically you're done so one thing that we need to talk about it two different ways that this might be shown I remember function notation is just when we have some find like FFX where G is at that's just a notation we could just as easily say instead of f of x equals 3x - 7 what is just as easily tie a y equals 3x - 7 has a don't let that that's have function notation body and you can have it fixed or geometric you that sir. Answer whatever text you back to Nature that sir probably are most common though but don't be surprised if you see all kinds on these exercises -7 and Gia that is 2x - 1 K will give two linear to linear functions here now what we're going to do with a composition of functions that around us a little bit do with a composition of functions is we are going to do something like this and first of all I need to tell you how we read this if I wrote this down we would read that as f Apache of it a lot of odds in there now you can also see that same thing written as f and sort of a little circular. There it's more play open g x and parenthesis exactly the same thing and we're going to do them the same whatever we might see however your exercises on IXL they are going to have it in this format right here okay now we could also have we could also find rather let's put it that way gif answer that okay and of course if we wanted to rewrite that we could also have noticed GIF okay so what we're going to come contrite on is this format because that's what you're going to see in your exercise it's okay but be aware that if you were to see this on maybe your sat or act or whatever you might take in the future whatever class set this means composition of functions as with an okay I love you just show you just in general with these two what a composition I do want I hear that the two are not going to be the same they should be according to what your your functions are but don't just look at him and say all it's all the same same letters and all the same function said it must be this time they're not necessarily in case they don't expect them today so let me just show you what I asked of G of X would be this year now all I'm going to do is I'm going to reply and to the s whatever G is queso whatever's first the axon that function is going to be replaced but a G of s so I'm going to go up here tonight I'm going to keep everything except for the at and in the place of that extra there I was going to put it in that see us and that is 2x - 1 and then I'm going to keep the rest of the fence I'm just keeping the ask Keith the first one keep everything about it except in place a debt to the end whatever your GF does that make sense to everyone and then from there we will just simplified to will do the distributive property so that gives a 6 x - 3 anime and we just simplified Stars we can so we end up with that's the composition of air hey that's all we have to do we're not doing anything else we're just simplifying that side and then of course it is they asked of G of x hey there buddy all right on that okay then let's go ahead and just do the other one here just to tell hey there they're not the same thing like I said they said this according to what you started out with the generally they are not going to be the same thing says it's time I think I can squeeze this in we have G of f of x I'm using the same functions up here but now this time notice my G comes first so I'm going to take whatever that function is something to take the two I'm going to keep it as he has put in place at the air I'm going to fit in 3x - 7 and then I'm going to keep the rest of the G so I need to keep that -1 so really I'm just substituting and I just need be careful on who what to substitute into what does that make sense to everyone and it should go ahead and distributes here and we are going to end up with sticks -14 - 1 and that is a stick that minus 50 Cent U not look at that site will I look pretty much alike they both have a six pack fana yeah but does this expression in sales is not the time or that 6x - 10 + 6 x - 15 or expression so don't expect them to be the same turn on some of these exercises I asked you to do one of them on some of them to ask you to do both of them it's just according to the situation okay I'll let that sort of thing hopefully that makes sense and of course you can do some hear they don't all have to be linear like cities but they certainly could be one exercise will be all linear but summer going to have some linear and some quadratic so we want to do with as well I remember pause your video when he needs to rewind it or whatever works for you okay alright let's see this let's go ahead and stay we've got to answer that is x squared plus 5 at angiovac C is for and now for the practice this time so let's go ahead and sign both of them let's find F of G of x and I'm going to ride it the way your exercises you're going to let's go over here and find G of f of it and we're just going to put a little line down the paper here and we'll try to keep ethos Dental different tax in okay all right that's something I find a subjective at I'm going to take my  it's going to stay the same except for the expedition answer the exes I'm in a substitute NZ G I bet hey so I'm going to have ads and it's Square therefore I'm going to replace you with for it but the x squared originally so yes I have to square the 4S got to swear the whole thing because that Forex is taking the place of that it plus I can't say it at is for it now and then we've got to finish up we've got a simplified we've got to clean it up if he will okay so if I take for it I swear it make sure you swear this for and the acts of 4 squared + 16 squared x I get x squared and then 5 * 4X is 20 plants that are those like terms can I add those can't do it can I because I can't add squares and exes okay so I'm absolutely through then I have found if of G okay does that make sense to everyone so wherever you have a nest and that asked how to be replaced with your other fence okay we all write on that coyote the G event for that I remember this time we're going to take airG and we are going to replace we're going to replace the excuse me in that with RS Yvette's so going to start down here with four times at but in place of the X I'm going to put my entire alphabet and my entire after that does x squared plus 5X now clean it up a little that we end up being with 4x squared plus 20 I want to be a cowboy some similarities but not exactly the same thing here okay alright everybody with me okay going to do one more and I'm going to do one more with a that quadratic simply because I want us to remember a couple of things here will not have a little bit more simplification to do with this one what is one of practices and probably have one or two they on your exercise for this but then time let's do our that is equal to x squared minus 2x Plus for work and cue that is 3x + 2 I'm just going to just write down the page because I may run out of room if I can large sometimes not run out of room if I try to split that page there is it since a little bit longer okay let's begin with our our Askew of it remember whichever one comes first which is the are in this k then I'm going to go through that are that and everywhere I seeing at I'm going to replace that we are cure that for the 3x plus fit so I got an Act 2 squared so I'm going to have to take 3 x + 6 + square it and that means to square the whole thing hey not just where the three astronauts wear that's it that's where the 3x + 6 the sun 2 I'm going to replace that  for 3 x + 6 and then Plusle don't forget you have to keep all of the other pieces if you will of of the function that you're working with take a look at that everybody's okay with it from here I need to simplify and we've talked about this before folks the 3x + 6 square and it's easy to leave out a part on that if we don't if we aren't careful so I'm going to suggest that you go down here to the bottom go to scratch sheet of paper somewhere and look at that and say okay 3x + 6 squared 3 + 10 * 3x + 6 and then but use their foil method let's just distributed so we've got four first outer comes out Ur weirdest Distributing at 3 at and then stick x 3 at and stick tunks it that'll be an ER and air last and then 3x x 3X is 9 x squared and 3X * 6 is 18x 6 * 3x is 18x and six times six is thirty-six if you'll do it like that she'll be a whole lot less likely to lose pieces if you will or to forget signs all right but we go ahead and simplify that that gives us 9 x squared + 36x + 36 we're just simple sign here the now can go up here and replace that 3x + 6 square with 9 x squared + 36 Army there + 36 I think you can kind of read that over here we're going to have to distribute so we have - 6 s + -12 + a + 4 simplify little bit farther so put some light terms together 32 set sun is 6s so we're going to have 9 x squared + 38 36 - 6 + + 36 - 12 + 4 + 36 - 12 is 24 + 4 is about a 28 that is remember if you ever catch me in a careless Sayre I write something down wrong or say something wrong or add or subtract or multiply or what please let me know we'll get that get that correct and you know it's easy for me to make careless mistakes sometimes you still need to do it before we all do it it's just human nature all right okay let's finish that one off then and let's use that same one and let's do it the other way around what's Duke u of R of f k i so I'm going to take our and that is x squared minus 2x + 4 and cue of that 3/8 + 10 and this time we are going to DQ of our of it and I think this one's going to not require quite as much maybe simplification okay so we can start with you so that's the one right here 3x + fit and in the place of the X we are going to put x squared minus 2x + 4 everything else this time so we have three and in place of it we will put quantity x squared minus 2x + 4 and and keep or left hi everybody good there after this point all I have to do is distribute that three and this one takes a little less time so have three x squared -6x + 12 + 6 3x squared at 6 a.m. put your lifetimes together 12 + 6 is 18 Edwards at Uniqua I noticed the difference in that one that one was cute of our vet this was our as q that a while ago but or definitely two different answers all right if you're going to have to exercise is on that for you just have to find acid yeah thats rrq that something like that and you're going to end up with an expression you're going to end up with something with excitant okay they can also ask you to find the value of that composition of functions stuff we can use the bottom here will save a little bit of paper the app to find SG or something like that or you're actually going to have to plug in a number let me show you how to do that it's not very difficult your calculator might come in handy let me get mine place here first one I'm going to do and I'm going to give you see you there 8 + 1 and did that is 3 it I'm going to give you a Siri linear functions fire what I'm going to ask you to find say pubg I saw in this time I'm going to instead of leaving it there replace the X with a v there are two different ways you can do it though you want and then you can also do do another approach if you prefer ants it's like I tell you all the time both of them are illegal do whichever one you want to say so let me tell you first of all what you could do okay you could find saved lyrics we did a while ago hey so you could do and I'm going to put that right here they India that and we would replace the and see you there with the deer that and I should have written that has see the cuz that's what we used to it and you could go ahead and okay I'm going to replace that  with my spread and get three yet a little bit get 3 apps and plays the DX and then plus one the last thing Isaiah that and then if you wanted to do see as d a v Dan you just replace the X with the V so you do 3 * 5 first one and that gives us be on 3 * 5 is 5015 + 1 is 610 to do with that why now one time you got to be careful with here and you got to realize when you get that 16 or 22 or whatever it is it don't look at it and tell a better / sides that is what you're finding your findings C of G of 5 and that is 15 so you are okay some ways to do it you can find the the composition of the Tucson option then plug the number in at the very end and some people like that there are other people that like it this way and I want to give you some options here Sandestin of the flats 10 times better than others at one thing you could do you could go ahead and find the five peso plug in deicide that will give you three times 5 just going to take the place of the ants with the fox hey so we got that so we've already found the just have to replace that with just so we are going to find it and look what we did we replace the S in RC with chain and we do 15 + 1 + of course 15 + 1 look what that Santa that gives us exactly the same as we got over here just a little bit different approach and it does matter which one you do I know this see you 15 but that is simply where I replace the Diaz V with the 15 there okay exchange whichever way you want to SRT lights to work with the numbers first then do that just fine whatever of 5 and then find C of that amount if you'd rather just go ahead and find the the whole polynomial with the variables in it and see if the event and then it's a very end plug that it tastes like your nazarena different people like different way my Tennessee sometimes has to do this one and substitute at the very straightforward person. but really it's just kind of up to the mood that I'm in at the month cabbage you use whichever one of course works for you okay and of course you can use your calculator on those according to how difficult it okay alright I want to do one more of those and I want to do one with a an exponent we're going to do a quadratic we're going to do one with the square and of course now should I go get the Sixth Sense DSM-5 not necessarily the same thing remember okay be careful with that event not the same thing as distilled at and it's the same thing as you plug in an Amber okay let's see this one last problem neon and then let's get need to work on Sunday then practice on that okay this time I'm sure that is 2x squared + 3 a&q that yeah 3X - 4 this time I've asked something a particular here I want to find Q octane off -3 octet of negative sure if we were in the classrooms I would probably look at you right now and say okay which one are we going to use or we can plug in and go about it that way or we going to find Q and I would have various various answers they are not probably pick the one that I heard first but I tell you what I think I'm going to do just so I can can mention something to you here just for me I'm going to go ahead and find p is -3 and then I'm going to find Q of whatever that is okay so I'm just going to come over here to the store and I'm going to find a of -3 so I'm going to go up here to Pay Here There and Everywhere I stand at I'm going to put in a negative 3 I wanted to do this when did this play because I was to remind you that we are replacing the ax with a negative 3 the app to square here so yes absolutely we must Square the negative 3 okay 3 * -3 squared + in death forget your + surf okay all right now use your order of operations use your calculator if you want to but please please please please please remember if you use your calculator make sure you put that -3 and parenthesis because remember it does exactly what you tell it stick so 2 * parentheses -3 squared Ambien + 3K and that's going to give us about a 21k but remember if you forget those parentheses around that negative it's going to give you something different so please be careful organic square that -3 okay set up a PS3 has given us a 21 so I'm just going to replace that pay is negative where was 21 block it off like that if you want to so now suddenly I have qx21 so I am basically done except for one last step I need to find Q 21 I'll replace it with 21 clear the queue and I've got three times 21 - 4 and that gives me a 63 - 4 + 63 - 4 fog delay I-59 now we're through at that point because we worked at down we found the PS3 we replaced it with 21 and we found q21 so we have actually found two of of -3 and the final solution for that the final answer I'm just going to ride is here 59 and remember we don't want to go ahead and say well I'll / 300 know or not variables there that is your value that composition of those two since when X is -3 okay does that make sense Atlas do the other way just in case you think you prefer that and let's make sure that they matched a sometimes we got Spencer sales so we're doing a q of pea vets first and then we will plug in our -3 right at the very end. if we're going to take you and we're going to go back up to Q we write everything down exactly as is except for the app and in place of the air we putting on our 2x squared + 3 so we are going to have three times the quantity 2 x squared + 3 and then don't forget that my hey there by see what we're doing tonight distribute that's going to give us text squared + 9 - 4 and then that gives us six x squared + 5 it's always got cheese I know your side while you ask for cube. So let's go ahead now let's find a of -3 so just got up a little bit there -3 and in places set timer 3 5 and 1/2 6 * -3 squared + 5 make sure you square the negative 3 put it in Firenze 3 squared it's not the six where we can let her calculator help us out so we've got it in position there we got six times a negative 3 squared and I didn't even put the time sign in there it will recognize that fit as a Time but make sure you swear that -3 and then plus 5K and that gives us 59 that was a exactly what we got 59 that was exactly what we got up here approaching it just a little bit different way but we should have ended up with exact if we have time sometimes remember it it's nice to do it one way and check it another or maybe we got started on one way and it was just too too the simplified we went back and put in the number first whichever way is fine and that's really just more of a account for a part on yours and and which way do you really prefer okay alright that's all I have on composition today I've got about 4 exercises for you to come with numbers some with just variable if you need me please reach out to me by email and your next lesson is going to be I am versus I think you're going to like those as well they're pretty straightforward but we need to be able to find the inverse of a function so I hope you all have a great week and work keep working really hard for me and let me know if you need me or if I can do anything for you? Or or if you just want to reach out and say hello thanks bye bye

Uploaded by Hattie Kilgore.

Videos

Composition of Functions

More videos from Hattie Kilgore