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how do you get the domain of this:

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

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Other answers:

√(x^2 - 9x +20)/√(x^2 - 5x + 6) I already know the domain. But, how do you get it?
first workout contraints for squareroot : the thing inside squareroot cannot be negative
next work out constraints for denominator : denominator cannot be equal to 0
consider numerator first : \(\sqrt{x^2 - 9x +20}\)
can u work out domain for that ?
{x|x>=5} is that right?
somewhat right :) lets see how to solve
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
thats one constraint for numerator, lets find out the constraints for denominator
ohhhh
I think I am starting to understand it :)
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
with those two things, we finished with the first step of finding constraints for radicals
so far we have this : x <= 4 or x >= 5 x <= 2 or x >= 3
yup, I understand it :)
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
w8 Isn't it that it should be: x >= 4 or x >= 5 x >= 2 or x >= 3 ???
lets combine all constraints and make a meaningful constraint
which one ?
(x-4)(x-5) >= 0 (x-2)(x-3) >= 0
oh i got ur question, il give quick explanation
you comfortable with parabola graph ?
I think so
il show u in graph why its x <=4 , x >=5
I know few things about parabola
ok
im sketching this parabola : (x-4)(x-5) >= 0
it intersect x axis at 4, 5 right ?
|dw:1348496600444:dw|
between 4 and 5, it is sinking down into x axis eh ?
its becoming NEGATIVE
|dw:1348496705657:dw|
why did it intersect in x axis at 4, 5?
when u factored you got : (x-4)(x-5)
that means it intersects x-axis at 4 and 5
ohh, ok what if it says (x-4)(x+5) does it intersect at 4 and -5 ?
thats right, when it says, (x-4)(x+5) = 0 then it intersects at 4 and -5
cuz for it to equal to 0, one of both of the factors must equal to 0
|dw:1348498226449:dw|
so the graph is like that?
perfect, thats (x-4)(x+5)
and the domain is x>=4,x<=-5 is it correct?
thats right ! you became expert ;p
for (x-4)(x+5)
Thanks! I know understand it. :) let's now continue with our previous discussion :)
great ! so far what we have
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
yeah we almost done
lets put down all the 3 constraints we got in one place :
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
I understand it. What's next?
see 2) and 3)
can we combine them as one, like this : 2) 3) : x < 2 or x > 3
I'll be back just continue.
someone is calling me
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
out of x < 2 & x <= 4, x < 2 is more restrictive, so we have this in our domain : \(\color{green}{x < 2}\)
out of x > 3 & x <= 4 x > 3 , x <= 4 , which is same as : \(\color{green}{3
and of course the last one, \(\color{green}{x >= 5}\)
sorry for being away, I'm here again :)
np :) see if above stuff makes sense
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}
yeah we always combine domain with "or" why ? cuz its meaningful. let me ask u a q
suppose we write : x < 2 and x >=5
for the domain it is ALWAYS "or" ?
is that possible ? can x be BOTH less than 2 and greater than 5 at the SAME time ha ?
yes always "or"
yes, it is not possible
is "1" less than 2 and greater than "5" ?
yeah, but if we put it like this : either "1" is less than 2 or greater than "5"
how meaningful it is, so while phrasing domain also, we use commonsense aswell :)
yes, Thank you very much for helping me :)
np i learned as well. i forgot these long back in college... i enjoyed going thru these again.. thnks you too :)

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