moongazer
  • moongazer
how do you get the domain of this:
Mathematics
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

moongazer
  • moongazer
http://www.wolframalpha.com/input/?i=domain+of+%E2%88%9A%28x%5E2+-+9x+%2B20%29%2F%E2%88%9A%28x%5E2+-+5x+%2B+6%29
moongazer
  • moongazer
how do you find it? step-by-step please :)
ganeshie8
  • ganeshie8
http://www.wolframalpha.com/input/?i=+%E2%88%9A%28x%5E2+-+9x+%2B20%29%2F%E2%88%9A%28x%5E2+-+5x+%2B+6%29

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

moongazer
  • moongazer
√(x^2 - 9x +20)/√(x^2 - 5x + 6) I already know the domain. But, how do you get it?
ganeshie8
  • ganeshie8
first workout contraints for squareroot : the thing inside squareroot cannot be negative
ganeshie8
  • ganeshie8
next work out constraints for denominator : denominator cannot be equal to 0
ganeshie8
  • ganeshie8
consider numerator first : \(\sqrt{x^2 - 9x +20}\)
ganeshie8
  • ganeshie8
can u work out domain for that ?
moongazer
  • moongazer
{x|x>=5} is that right?
ganeshie8
  • ganeshie8
somewhat right :) lets see how to solve
ganeshie8
  • ganeshie8
x^2-9x+20 >= 0 x^2-4x-5x+20 >=0 x(x-4) -5(x-4) >= 0 (x-4)(x-5) >= 0 x <= 4 or x >= 5
ganeshie8
  • ganeshie8
thats one constraint for numerator, lets find out the constraints for denominator
moongazer
  • moongazer
ohhhh
moongazer
  • moongazer
I think I am starting to understand it :)
ganeshie8
  • ganeshie8
good :) since, denominator is also under radical, it must be >=0 : x^2 - 5x + 6 >= 0 x^2-3x-2x + 6 >= 0 x(x-3) -2(x-3) >= 0 (x-2)(x-3) >= 0 x <= 2 or x >= 3
ganeshie8
  • ganeshie8
with those two things, we finished with the first step of finding constraints for radicals
ganeshie8
  • ganeshie8
so far we have this : x <= 4 or x >= 5 x <= 2 or x >= 3
moongazer
  • moongazer
yup, I understand it :)
ganeshie8
  • ganeshie8
next one is denominator can never equal to 0. so, x^2 - 5x + 6 \(\ne\) 0 x^2-3x-2x + 6 \(\ne\) 0 x(x-3) -2(x-3) \(\ne\) 0 (x-2)(x-3) \(\ne\) 0 x \(\ne\) 2 or x \(\ne\) 3
moongazer
  • moongazer
w8 Isn't it that it should be: x >= 4 or x >= 5 x >= 2 or x >= 3 ???
ganeshie8
  • ganeshie8
lets combine all constraints and make a meaningful constraint
ganeshie8
  • ganeshie8
which one ?
moongazer
  • moongazer
(x-4)(x-5) >= 0 (x-2)(x-3) >= 0
ganeshie8
  • ganeshie8
oh i got ur question, il give quick explanation
ganeshie8
  • ganeshie8
you comfortable with parabola graph ?
moongazer
  • moongazer
I think so
ganeshie8
  • ganeshie8
il show u in graph why its x <=4 , x >=5
moongazer
  • moongazer
I know few things about parabola
moongazer
  • moongazer
ok
ganeshie8
  • ganeshie8
im sketching this parabola : (x-4)(x-5) >= 0
ganeshie8
  • ganeshie8
it intersect x axis at 4, 5 right ?
ganeshie8
  • ganeshie8
|dw:1348496600444:dw|
ganeshie8
  • ganeshie8
between 4 and 5, it is sinking down into x axis eh ?
ganeshie8
  • ganeshie8
its becoming NEGATIVE
ganeshie8
  • ganeshie8
|dw:1348496705657:dw|
moongazer
  • moongazer
why did it intersect in x axis at 4, 5?
ganeshie8
  • ganeshie8
when u factored you got : (x-4)(x-5)
ganeshie8
  • ganeshie8
that means it intersects x-axis at 4 and 5
moongazer
  • moongazer
ohh, ok what if it says (x-4)(x+5) does it intersect at 4 and -5 ?
ganeshie8
  • ganeshie8
thats right, when it says, (x-4)(x+5) = 0 then it intersects at 4 and -5
ganeshie8
  • ganeshie8
cuz for it to equal to 0, one of both of the factors must equal to 0
moongazer
  • moongazer
|dw:1348498226449:dw|
moongazer
  • moongazer
so the graph is like that?
ganeshie8
  • ganeshie8
perfect, thats (x-4)(x+5)
moongazer
  • moongazer
and the domain is x>=4,x<=-5 is it correct?
ganeshie8
  • ganeshie8
thats right ! you became expert ;p
moongazer
  • moongazer
for (x-4)(x+5)
moongazer
  • moongazer
Thanks! I know understand it. :) let's now continue with our previous discussion :)
ganeshie8
  • ganeshie8
great ! so far what we have
moongazer
  • moongazer
next one is denominator can never equal to 0. so, x^2 - 5x + 6 ≠ 0 x^2-3x-2x + 6 ≠ 0 x(x-3) -2(x-3) ≠ 0 (x-2)(x-3) ≠ 0 x ≠ 2 or x ≠ 3
ganeshie8
  • ganeshie8
yeah we almost done
ganeshie8
  • ganeshie8
lets put down all the 3 constraints we got in one place :
ganeshie8
  • ganeshie8
1) numerator radical : x <= 4 or x >= 5 2) denominator radical : x <= 2 or x >= 3 3) denominator cant be 0 : x ≠ 2 or x ≠ 3
moongazer
  • moongazer
I understand it. What's next?
ganeshie8
  • ganeshie8
see 2) and 3)
ganeshie8
  • ganeshie8
can we combine them as one, like this : 2) 3) : x < 2 or x > 3
moongazer
  • moongazer
I'll be back just continue.
moongazer
  • moongazer
someone is calling me
ganeshie8
  • ganeshie8
ok after combining 2) and 3) we are left with : 1) numerator radical : x <= 4 or x >= 5 2) x < 2 or x > 3 this is the last step. see if u can figure out
ganeshie8
  • ganeshie8
out of x < 2 & x <= 4, x < 2 is more restrictive, so we have this in our domain : \(\color{green}{x < 2}\)
ganeshie8
  • ganeshie8
out of x > 3 & x <= 4 x > 3 , x <= 4 , which is same as : \(\color{green}{3
ganeshie8
  • ganeshie8
and of course the last one, \(\color{green}{x >= 5}\)
moongazer
  • moongazer
sorry for being away, I'm here again :)
ganeshie8
  • ganeshie8
np :) see if above stuff makes sense
moongazer
  • moongazer
it makes sense but why in the final answer they used "or" not "and" "," "then" or anything else dom K: {x|x<2 or 3=5}
ganeshie8
  • ganeshie8
yeah we always combine domain with "or" why ? cuz its meaningful. let me ask u a q
ganeshie8
  • ganeshie8
suppose we write : x < 2 and x >=5
moongazer
  • moongazer
for the domain it is ALWAYS "or" ?
ganeshie8
  • ganeshie8
is that possible ? can x be BOTH less than 2 and greater than 5 at the SAME time ha ?
ganeshie8
  • ganeshie8
yes always "or"
moongazer
  • moongazer
yes, it is not possible
ganeshie8
  • ganeshie8
is "1" less than 2 and greater than "5" ?
ganeshie8
  • ganeshie8
yeah, but if we put it like this : either "1" is less than 2 or greater than "5"
ganeshie8
  • ganeshie8
how meaningful it is, so while phrasing domain also, we use commonsense aswell :)
moongazer
  • moongazer
yes, Thank you very much for helping me :)
ganeshie8
  • ganeshie8
np i learned as well. i forgot these long back in college... i enjoyed going thru these again.. thnks you too :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.