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all right what I like to do is a show
you how to find the thing made of a
problem like this no domain is very
tricky with us and one thing we're
finding domain couple things we need to
think about remember a function is when
you have an input value and you're able
to find an output that and that's what
we say is for it is defined for an
alphabet meaning if you put an input
value in you're going to get an output
value so there are a couple instances
though however when we plug in an input
value and there is no output value for
instance let's just set it f of X if I
did 3 over X well the only value that
this does not work for is when X is
equal to 0 because when x equals 0 I
have 3 divided by 0 and you cannot
divide 0 into a number so therefore we
write X cannot equal 0 so the domain for
this function I was gonna write the
domain it's gonna be all real numbers
all numbers negative 5 negative 13 107
all numbers work except for 0 so when
we're trying to find the domain of a
rational function what we want to do is
we want to find out what values making 0
on the bottom so here I have a quadratic
expression so I need to figure out x
squared plus 8x
plus 15 equals zero I want to figure out
what values can I find for X that are
going to make this function zero so when
we have a quadratic it's a little bit
difficult it's not like a regular linear
equation where you can just solve for x
we're gonna have to do some type of
either squaring or factoring since I
have two x's I know that I'm going to
want to do factor so what type of
factoring I want to do well here my a is
equal to 1 B is equal to 8 and C is
equal to 15 so a lot of times what I'll
do is always take my 8 times C which is
1 times 15 and I'll take my B which is 8
and I'm just gonna systematically think
of what two numbers multiply to give me
15 but add to give me 8 and those
answers are gonna be 3 and 5 so
therefore I can factor this to be X plus
3 times X plus 5 equals 0 and if I was
to foil this back out I would get this
expression now either one of these
multiply to give me 0 so therefore one
of these has to be 0
so you can say X plus 3 equals 0 or X
plus 5 equals 0 therefore if subtract 3
if X is equal to negative 3 this problem
equals 0 or if X is equal to a negative
by this problem sequels here so if you
were to plug in negative 3 into there
you would get 0 if you're plugging in
negative 5 into this equation you would
get 0 so therefore my domain for this
problem
is going to be all real numbers except X
cannot equal a negative three and a five
so when you're defining the domain
especially the rational expression you
want to see what numbers can't we use
and the numbers you can't use are the
numbers that are going to make our
denominator zero
