Question

how do you get the domain of this:

Answer 1

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

Answer 2

how do you find it? step-by-step please :)

Answer 3

http://www.wolframalpha.com/input/?i=+%E2%88%9A%28x%5E2+-+9x+%2B20%29%2F%E2%88%9A%28x%5E2+-+5x+%2B+6%29

Answer 4

√(x^2 - 9x +20)/√(x^2 - 5x + 6)
I already know the domain. But, how do you get it?

Answer 5

first workout contraints for squareroot : the thing inside squareroot cannot be negative

Answer 6

next work out constraints for denominator : denominator cannot be equal to 0

Answer 7

consider numerator first : \(\sqrt{x^2 - 9x +20}\)

Answer 8

can u work out domain for that ?

Answer 9

{x|x>=5} is that right?

Answer 10

somewhat right :)

lets see how to solve

Answer 11

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

Answer 12

thats one constraint for numerator, lets find out the constraints for denominator

Answer 13

ohhhh

Answer 14

I think I am starting to understand it :)

Answer 15

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

Answer 16

with those two things, we finished with the first step of finding constraints for radicals

Answer 17

so far we have this :

x <= 4 or x >= 5
x <= 2 or x >= 3

Answer 18

yup, I understand it :)

Answer 19

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

Answer 20

w8 Isn't it that it should be:
x >= 4 or x >= 5
x >= 2 or x >= 3
???

Answer 21

lets combine all constraints and make a meaningful constraint

Answer 22

which one ?

Answer 23

(x-4)(x-5) >= 0
(x-2)(x-3) >= 0

Answer 24

oh i got ur question, il give quick explanation

Answer 25

you comfortable with parabola graph ?

Answer 26

I think so

Answer 27

il show u in graph why its x <=4 , x >=5

Answer 28

I know few things about parabola

Answer 29

ok

Answer 30

im sketching this parabola :

(x-4)(x-5) >= 0

Answer 31

it intersect x axis at 4, 5 right ?