Algebraically finding the domain

[kenhung123]

You know how in the video he says if x>2 then x is definately >-5 but what if x is (-5,2)?

[Blakhitman]

That cant be the case since the condition is x is greater than 2

[kenhung123]

Yea but he said if x>2 then x is definitely >-5 so he just took away x>-5 and used x>2
But that isn't entirely true as x>-5 includes values from which x includes: (-5,2) but x>2 doesn't

[Blakhitman]

I don't see where you're going with this.

He's saying if x is greater than -5 AND x is also greater than 2 than there's no point in having x greater than -5 as x > 2 obviously means that x> -5...

Sorry if I'm misunderstanding.

[the.watchman]

I don't see where you're going with this.

He's saying if x is greater than -5 AND x is also greater than 2 than there's no point in having x greater than -5 as x > 2 obviously means that x> -5...

Sorry if I'm misunderstanding.

Yes, note the AND, not OR

The intersection of x>-5 and x>2 is x>2
x can't equal a number between -5 and 2, because then the ineqns are not both satisfied

[kenhung123]

See below

[Blakhitman]

yep and hence (-5,2) is not defined as watchman said, it needs to satisfy both inequations.

[m@tty]

We want the intersection of the two sets, that is the elements present in both. As are only present on one of the lines it is discarded.


EDIT:
If we wanted the union then we take all elements of both sets, and as you said would be

[Blakhitman]

using the video's example

must be greater than 0

if we sub in a point in the domain you specified, say for example -2, then

we will get -12 but that is not greater than 0!!!!!! so x cannot equal -2!!!!!!!

[kenhung123]

Right. I got it now, so we are finding what is common to both.

Thanks for help guys!

[m@tty]

Yes! No problem