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Good day students welcome to mathgotserved.com in this clip were going to be going over how to find the domain of composite functions right so let's go ahead and write down the all instructions we are to find find the domain of F compose with G of X where F of X is equal to three divided by X this to and G of X is for over X okay now before we go ahead and solve this problem is about domain real quick Om domain basically involves the set of all inputs that guarantees is defined or real outputs okay so any impact value in a function that results in an imaginary or undefined outputs those values are normally excluded from the domain of the function okay so for example if you have the square roots of a negative number square of negative that yields an imaginary number right let's imaginary and this is normally excluded from the domain also when you divide by zero what's your answer division by zero result in undefined outputs so that is also on excluded from the domain so if you have the square roots let's see how the square root of the function of functions you a family have the situation you want to take erratic X you and stated to be greater than or equal to zero F on so for the domain involving radicals if you have irrational is expression let's see how Kubrick you what you do is you take the denominator and said it not to be equal to zero I so these are have basically what some of the way to find the domain of functions the other function out there to have restriction under domains.com use of two common ones were going to be focusing on okay so let's take a look at this problem now when you finding the domain of a composite function what you going to do is you going to find the union on of two domain okay so there may procedure is to confine that you neon of two things union the input function G and that of G and union of the domain started domain of G union of the domain of G of G and the domain of the composite function F of G of X right so basically have to problems in one first there were going to do is find the domain restrictions G and there were going to compose this two functions and find the domain of that that unites to two results and that will give us our domain our right so let's break it up this is one in this is to so part one we going to find the domain of the inner function domain of G now on earth so I do that G is the inner function well you look at this notation right here at composing G of X weather that mean F compose with G of X simply means that we taking G and plug-in it into F so this is F of G of X so we find a of domain of the composition of two functions you take the inner function G of X and find that domain verse okay so the inner function in this problem is former X so we need to find the domain of over X G of X is former X now when you dealing with a rational function which is a function the have the variable in the denominator what you simply do as indicated here is you set the denominator equal to zero so the denominator here is X equal to zero so this is a restriction this value results in undefined outputs of X cannot be equal to zero right so this is one of the restrictions of our domain we done with the first parts which is finding the domain of G what are we going to do next we going to find the domain of F of G of X okay that's what were going to do next right so in other for us to do that we need to find what F of G of X is okay so one of find the domain of the compose function F of G of X okay so what is the, F of G of X is go ahead and figure out what that is F of X the outer function is three divided by X plus two now to find F of G with that substitute the inputs with another functions of the out X three divided by parenthesis is plus two now let's take a minute a look at what just happened here the outer function at X is here taking of the axes why did I do that while because I want to find F of G of X which is the same unit F compose with G of X in the same thing so G is former X so that the name of the function on the left in the volume the function on the right okay so this is your compose function right here three divided by four over X plus two okay now I can simplified is further but that's the message remember one we want to find the domain so what is the domain of this function right here we have a rational function so what you do is you take the denominator for over X this to the denominator cannot be what's the denominator cannot zero okay so let's all this equation that will tell of the restriction of X that we need to consider so here we going to subtract from both sides so subtract to you have four over X equals negative two and then were going to set this over one so we have to fractions it across multiply multiply what sites by X you going to end up with negative X

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