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How do I: Express the domain of the given function using interval notation? f(x)=x/ 15x^2 + 13x - 20

Mathematics
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hey. do you mean f(x) = x / (15x^2 + 13x - 20) ?
yes
nevermind i solved it thanks

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Other answers:

i meant to ask a different question, sorry
is there another question you want to ask?
yes. it was determine domain and range using interval notation of f(x)= radicand(x^2 -8x -9
\[f(x) = \sqrt{x^2 -8x -9}\]
just so you know i believe radicand refers to what is under the square root, but you mean square root of (x^2 -8x -9) right?
ok well for a square root function what you need to know is that what's under the square root can't be negative, because no real number multiplied by itself equals a negative
ok i understand so far
ok, so you want to try to factor that, to see where it is negative and where it is positive. you did the other problem so you know how to factor, right?
yes, i have x=-9 and x=1
that's not quite right, look at it again
is it 9 and -1 instead?
sorry, my browser crashed. yes, that's right. so you have sqrt ((x-9)(x+1)). what i like to do is draw a number line below that to help me see where the function is 0, negative, and positive
so draw a line, hashmarks at -1 and 9, and we know it's 0 at those points, so mark 0 above -1 and 9
now test a point on the left side, in the middle, and on the right to see if it comes up positive or negative
try x= -2. (-2-9)(-2+1) is a negative times a negative, so that's positive. so now i mark all +++ to the left of the first 0 on my line
you still here, is this helping?
im here thank you. how do you know what sign to use when determining if the equation is true?
what i mean is, you plug in -2 to the equation to see if its true right?
what do you mean by true?
(-2)^2 - 8(-2) -9=0 ?
or do you use an equality sign
no, we already know that the values that make what's under the square root equal to 0 are x = -1 and x = 9
that's what the factoring is for
by plugging in -2, we just want to see if that section of x-values comes up negative for y or positive
oh ok
remember the goal is to see which x-values make what's under the square root negative, because those are not part of the domain
so by plugging in -2, we get 11. then what from there?
it doesn't matter what the number is, we just care that it's positive, so did you draw the number line like i said? do you understand what i mean by that?
yes
so since they're both positive, that means what for interval notation?
well -2 turned out positive, so that means that all values less than -1 turn out positive, so those will be part of the domain
but we still have to check the other intervals
the one in the middle comes out negative
and the last one comes out positive
yes that's right, so the domain is the positive part
ok so what does it look like in interval form?
ok (-inf, -1) U (9, inf) is what it will be
(-infinity,-1] [9,infinity)? something like that?
no, you're right
the brackets are right. (-inf, -1] U [9, inf) the U stands for union
got it! thank you for your help!
:)
no problem.

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