anonymous
  • anonymous
How do I: Express the domain of the given function using interval notation? f(x)=x/ 15x^2 + 13x - 20
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
hey. do you mean f(x) = x / (15x^2 + 13x - 20) ?
anonymous
  • anonymous
yes
anonymous
  • anonymous
nevermind i solved it thanks

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anonymous
  • anonymous
i meant to ask a different question, sorry
anonymous
  • anonymous
is there another question you want to ask?
anonymous
  • anonymous
yes. it was determine domain and range using interval notation of f(x)= radicand(x^2 -8x -9
anonymous
  • anonymous
\[f(x) = \sqrt{x^2 -8x -9}\]
anonymous
  • anonymous
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?
anonymous
  • anonymous
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
anonymous
  • anonymous
ok i understand so far
anonymous
  • anonymous
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?
anonymous
  • anonymous
yes, i have x=-9 and x=1
anonymous
  • anonymous
that's not quite right, look at it again
anonymous
  • anonymous
is it 9 and -1 instead?
anonymous
  • anonymous
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
anonymous
  • anonymous
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
anonymous
  • anonymous
now test a point on the left side, in the middle, and on the right to see if it comes up positive or negative
anonymous
  • anonymous
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
anonymous
  • anonymous
you still here, is this helping?
anonymous
  • anonymous
im here thank you. how do you know what sign to use when determining if the equation is true?
anonymous
  • anonymous
what i mean is, you plug in -2 to the equation to see if its true right?
anonymous
  • anonymous
what do you mean by true?
anonymous
  • anonymous
(-2)^2 - 8(-2) -9=0 ?
anonymous
  • anonymous
or do you use an equality sign
anonymous
  • anonymous
no, we already know that the values that make what's under the square root equal to 0 are x = -1 and x = 9
anonymous
  • anonymous
that's what the factoring is for
anonymous
  • anonymous
by plugging in -2, we just want to see if that section of x-values comes up negative for y or positive
anonymous
  • anonymous
oh ok
anonymous
  • anonymous
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
anonymous
  • anonymous
so by plugging in -2, we get 11. then what from there?
anonymous
  • anonymous
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?
anonymous
  • anonymous
yes
anonymous
  • anonymous
so since they're both positive, that means what for interval notation?
anonymous
  • anonymous
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
anonymous
  • anonymous
but we still have to check the other intervals
anonymous
  • anonymous
the one in the middle comes out negative
anonymous
  • anonymous
and the last one comes out positive
anonymous
  • anonymous
yes that's right, so the domain is the positive part
anonymous
  • anonymous
ok so what does it look like in interval form?
anonymous
  • anonymous
ok (-inf, -1) U (9, inf) is what it will be
anonymous
  • anonymous
(-infinity,-1] [9,infinity)? something like that?
anonymous
  • anonymous
no, you're right
anonymous
  • anonymous
the brackets are right. (-inf, -1] U [9, inf) the U stands for union
anonymous
  • anonymous
got it! thank you for your help!
anonymous
  • anonymous
:)
anonymous
  • anonymous
no problem.

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