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 equals for divide both sides by negative
to and you final answer is X equals negative two write X equals negative two so this is
the second constraint on your domain right so X cannot be negative to or a to have zero
in the denominator okay I so what is our final answer remember we are to unites the domain
of G and the domain of the compose function okay so that X cannot be zero and X cannot
be negative to so our domain is set X such that X cannot be negative to and we dividing
the union here so is of four and X cannot be zero okay so this is the domain of our
composite composite function F of G of X thanks so much for taking the time to watch this
presentation really appreciated the free to subscribe to our channel for updates to other
cool tutorials such as this more clips,, mathgotserved.com any there any lessons you like us to make
for you what you have any questions or comments to free to included in the comments section
below this box thanks again for watching and have a wonderful day

• ### maths gotserved

Great presentation. Crystal clear explanation.

great job

• ### Tom Mitchell

in the example you gave how would you work out the same question but with the functions swapped so f is g and g is f

nicely done!

• ### Meli Lightyear

thank you so much!

• ### Jordan Hudson

how did you go from 4/x = -2/1 to -2x=4

• ### Erik Martines Sanches

Hi, thanks for this one.

Interesting, I see you unioned the domain of f and f(g). I didn't know you could do that.

My calc book (Calculus 7th Ed, Adams, page 35) states that most of combinations of f and g have domains that intersect the domains of f and g.

So can the domain of f(g) = {x | x != -2 and x != 0} be thought of as the intersection of the domain for f = {x | all Reals, x != -2} and the domain for g = {x | all Reals, x != 0 }? I think so ðŸ™‚

Good Job!

• ### cenotal studio

what happened to 3

wow. ive tried for about an hour looking for different videos and finally found this one. i understand this so clearly now! thank you very very much!!!!!!

Good

• ### Goofy

Fuck I hate math

• ### Moon Child

This is a great explanation, it cuts off a lot of time. But it only works in certain situations.

• ### Rosemarie Dagohoy

What if you're going to solve it all of the operation?

• ### D3ATH G4MING

Omg your amazing sir! Our gen math teacher sucks ass, she teaches us wrong lessons like her domain has (><) and shits.

• ### anna baudelaire

how to write in interval notation?

• ### Anonymous

this helped a lot! thank you.

• ### Curtis Choi

Thanks man really helped! <3

• ### Rajendra Misir

I like your logical, patient and clear explanation. Your technique is simple and easy to follow and understand. Thanks Sir.

• ### xCAMRENx

tangina bobo ko talaga