finding domain of rational functions algebraically college algebra #1
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finding domain of rational functions algebraically college algebra #1


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
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