Good day students welcome to mathgotserved.com

in this clip were going to be going over the second example on how to find the domain of

rational functions algebraic we okay so let’s take a look at the directions for the example

we are to find the domain of the following rational function so for number two we have

the rational function F of X equals two X times X minus three divided by X was three

times two X minus three okay so indicate it in problem number one if you want to find

the domain of a rational function of this nature all you have to do is find the value

of X value or values of X that causes the entire expression to be undefined so what

causes and expression to be undefined any value that causes the denominator to have

a value of zero result in the entire expression becoming undefined okay so our focus will

be or should be on the denominator so when you look in our the domain the rational function

we just have to do is so for when the denominator is equal to zero and you are going to exclude

the answer is from your domain okay it does values are excluded from the domain you guaranteed

to have is defined outputs for all your inputs right so take a look at this example what

is the denominator the denominator is the product of these two quantities X was three

times two X minus three okay so said it equal to zero and then we’ll solve this graphic

equation one assault is that the quadratic equation our answer is shift be excluded from

the domain and will have the domain on this function right so how do we so the quadratic

equation in fact other for to solve this one apply the zero product property okay just

basically says that is the product of two numbers are is zero then one of the numbers

have to be zero okay so you X was three is equal to zero or two X minus three is equal

to zero are isolate going to have two values to be excluded from the domain of this function

right here let’s all the first one subtract three from both sides X equals negative three

and then take a look at the second equation all you do is you look at three to both sides

in divide by two okay so is go ahead and do this as three to both sides that yields two

X equals positive three and then divide both sides by two that will isolate express and

then we’ll have X equals three over to write so the question is what these two values mean

what is this me well these two values when you plug it into this function you will have

on defined outputs so that means those numbers have to be excluded from the domain right

so how do we write our final answer is going to write down the domain is the set of X is

such that X cannot the negative three and X cannot be three over to okay and any other

value you and eight defined outputs for this function so the domain restricts X is so everything

apart from these values right here so X cannot be the/there X cannot be negative three and

X cannot be three over to so that’s the domain of our function right so that’s that the thanks

so much for taking the time to watch this presentation really appreciated the free to

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## 13 Comments

## vince ifezue

thanks

## vince ifezue

Can i contact you for more tutorial ?

## Ineed hugspls

What if its the 3x+5 is the numerator and 14x is the denominator?

## Krystal Suyod

what if the denominator is 2x²+1?

## Kevin D

interval notation is maybe [-5/3 , oo) right?

## Erika Claudia

how to solve this? g(x)=4/x^2-25

## Alex Rojas

life saver

## 10,000 subscribers with no videos Challenge

What a Beaut

## Ben

thanks, I just needed an more complex example yours worked. Nice English, keep it up and don't try to stress the pronunciation so much- let it flow, you are very good.

## Kaye Garcia

how to determine domain and range of the relation M={(x,y)|y=x²+5x+4}???

## Lovely Ley

My denominator is 8x and it’s hard because there’s no example with one term😩

## xjustchillx

I don’t know how but I came up with this in math class since I was bored (my math teacher sucks at teaching), so instead of doing this, the easiest way of explaining this is that you factor the denominator, and once your finished with that, you change the symbol of the second term. Ex: The denominator is (x*2+5x+6). When you factor that you will get (x+3)(x+2), change the symbol of the second term so the restricted values become [-3, -2]. If the denominator has only one term (ex: 7x), then x=0. I don’t know if this is correct, it’s probably wrong since I’m just at grade 8, but it works for me so 🤷♀️🤷♀️.

## Catherine Castro

Dang it took me so much time in finding the right video to watch!!!then finally i found it!!! Thank u so much