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moongazer
 2 years ago
Best ResponseYou've already chosen the best response.1how do you find it? stepbystep please :)

moongazer
 2 years ago
Best ResponseYou've already chosen the best response.1√(x^2  9x +20)/√(x^2  5x + 6) I already know the domain. But, how do you get it?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1first workout contraints for squareroot : the thing inside squareroot cannot be negative

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1next work out constraints for denominator : denominator cannot be equal to 0

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1consider numerator first : \(\sqrt{x^2  9x +20}\)

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1can u work out domain for that ?

moongazer
 2 years ago
Best ResponseYou've already chosen the best response.1{xx>=5} is that right?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1somewhat right :) lets see how to solve

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1x^29x+20 >= 0 x^24x5x+20 >=0 x(x4) 5(x4) >= 0 (x4)(x5) >= 0 x <= 4 or x >= 5

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1thats one constraint for numerator, lets find out the constraints for denominator

moongazer
 2 years ago
Best ResponseYou've already chosen the best response.1I think I am starting to understand it :)

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1good :) since, denominator is also under radical, it must be >=0 : x^2  5x + 6 >= 0 x^23x2x + 6 >= 0 x(x3) 2(x3) >= 0 (x2)(x3) >= 0 x <= 2 or x >= 3

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1with those two things, we finished with the first step of finding constraints for radicals

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1so far we have this : x <= 4 or x >= 5 x <= 2 or x >= 3

moongazer
 2 years ago
Best ResponseYou've already chosen the best response.1yup, I understand it :)

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1next one is denominator can never equal to 0. so, x^2  5x + 6 \(\ne\) 0 x^23x2x + 6 \(\ne\) 0 x(x3) 2(x3) \(\ne\) 0 (x2)(x3) \(\ne\) 0 x \(\ne\) 2 or x \(\ne\) 3

moongazer
 2 years ago
Best ResponseYou've already chosen the best response.1w8 Isn't it that it should be: x >= 4 or x >= 5 x >= 2 or x >= 3 ???

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1lets combine all constraints and make a meaningful constraint

moongazer
 2 years ago
Best ResponseYou've already chosen the best response.1(x4)(x5) >= 0 (x2)(x3) >= 0

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1oh i got ur question, il give quick explanation

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1you comfortable with parabola graph ?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1il show u in graph why its x <=4 , x >=5

moongazer
 2 years ago
Best ResponseYou've already chosen the best response.1I know few things about parabola

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1im sketching this parabola : (x4)(x5) >= 0

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1it intersect x axis at 4, 5 right ?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1348496600444:dw

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1between 4 and 5, it is sinking down into x axis eh ?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1its becoming NEGATIVE

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1348496705657:dw

moongazer
 2 years ago
Best ResponseYou've already chosen the best response.1why did it intersect in x axis at 4, 5?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1when u factored you got : (x4)(x5)

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1that means it intersects xaxis at 4 and 5

moongazer
 2 years ago
Best ResponseYou've already chosen the best response.1ohh, ok what if it says (x4)(x+5) does it intersect at 4 and 5 ?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1thats right, when it says, (x4)(x+5) = 0 then it intersects at 4 and 5

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1cuz for it to equal to 0, one of both of the factors must equal to 0

moongazer
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1348498226449:dw

moongazer
 2 years ago
Best ResponseYou've already chosen the best response.1so the graph is like that?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1perfect, thats (x4)(x+5)

moongazer
 2 years ago
Best ResponseYou've already chosen the best response.1and the domain is x>=4,x<=5 is it correct?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1thats right ! you became expert ;p

moongazer
 2 years ago
Best ResponseYou've already chosen the best response.1Thanks! I know understand it. :) let's now continue with our previous discussion :)

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1great ! so far what we have

moongazer
 2 years ago
Best ResponseYou've already chosen the best response.1next one is denominator can never equal to 0. so, x^2  5x + 6 ≠ 0 x^23x2x + 6 ≠ 0 x(x3) 2(x3) ≠ 0 (x2)(x3) ≠ 0 x ≠ 2 or x ≠ 3

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1lets put down all the 3 constraints we got in one place :

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.11) 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
 2 years ago
Best ResponseYou've already chosen the best response.1I understand it. What's next?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1can we combine them as one, like this : 2) 3) : x < 2 or x > 3

moongazer
 2 years ago
Best ResponseYou've already chosen the best response.1I'll be back just continue.

moongazer
 2 years ago
Best ResponseYou've already chosen the best response.1someone is calling me

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1ok 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
 2 years ago
Best ResponseYou've already chosen the best response.1out of x < 2 & x <= 4, x < 2 is more restrictive, so we have this in our domain : \(\color{green}{x < 2}\)

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1out of x > 3 & x <= 4 x > 3 , x <= 4 , which is same as : \(\color{green}{3<x\le 4}\)

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1and of course the last one, \(\color{green}{x >= 5}\)

moongazer
 2 years ago
Best ResponseYou've already chosen the best response.1sorry for being away, I'm here again :)

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1np :) see if above stuff makes sense

moongazer
 2 years ago
Best ResponseYou've already chosen the best response.1it makes sense but why in the final answer they used "or" not "and" "," "then" or anything else dom K: {xx<2 or 3<x<=4 or x>=5}

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1yeah we always combine domain with "or" why ? cuz its meaningful. let me ask u a q

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1suppose we write : x < 2 and x >=5

moongazer
 2 years ago
Best ResponseYou've already chosen the best response.1for the domain it is ALWAYS "or" ?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1is that possible ? can x be BOTH less than 2 and greater than 5 at the SAME time ha ?

moongazer
 2 years ago
Best ResponseYou've already chosen the best response.1yes, it is not possible

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1is "1" less than 2 and greater than "5" ?

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1yeah, but if we put it like this : either "1" is less than 2 or greater than "5"

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1how meaningful it is, so while phrasing domain also, we use commonsense aswell :)

moongazer
 2 years ago
Best ResponseYou've already chosen the best response.1yes, Thank you very much for helping me :)

ganeshie8
 2 years ago
Best ResponseYou've already chosen the best response.1np i learned as well. i forgot these long back in college... i enjoyed going thru these again.. thnks you too :)
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