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System Message

[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Guest (Customer)

[00:00:00] i was supposed to find the inverse of this and determine its domain and range. i found the inverse but im having trouble determining the domain and range. Please help me?

Jose L (Tutor)

[00:00:03] Hi.
Welcome to Tutor.com .
I see your problem.
Were you able to start it?

Guest (Customer)

[00:00:12] yes

Jose L (Tutor)

[00:00:16] ok great

[00:00:20] what do you have so far?

Guest (Customer)

[00:00:39] so i found the inverse. like i
know the steps to get tht so ill
write what i got

Jose L (Tutor)

[00:00:45] ok

Guest (Customer)

[00:01:18] thats what i got

Jose L (Tutor)

[00:01:32] let me check..working it here

Guest (Customer)

[00:01:41] ok

Jose L (Tutor)

[00:01:57] ok well it's +8 since the -8 is moved to the other side

[00:02:07] questions on that?

Guest (Customer)

[00:02:19] no i just wrote it wrong, sorry!

Jose L (Tutor)

[00:02:22] oh ok

[00:02:37] know how to find the domain?

Guest (Customer)

[00:03:14] umm do i just put x^2+8 is
less than or equal to 0?

[00:03:20] like solve tht?

Jose L (Tutor)

[00:03:25] well we have an ..odd...root

[00:03:35] we can find roots of negative numbers

[00:03:40] when the root is odd

[00:03:44] for example

[00:03:50] cube root of -8 = -2

[00:04:03] so there are not restrictions for odd roots

[00:04:09] we can use any real number

[00:04:20] no* restrictions

Guest (Customer)

[00:04:28] ok]

Jose L (Tutor)

[00:04:32] questions on the domain?

Guest (Customer)

[00:04:38] no

Jose L (Tutor)

[00:04:44] know how to find the range?

Guest (Customer)

[00:04:53] no

Jose L (Tutor)

[00:05:04] if x=0

[00:05:12] what answer do you get?

Guest (Customer)

[00:05:17] 0?

Jose L (Tutor)

[00:05:45] 0^2 + 8 = ?

Guest (Customer)

[00:05:56] 8

Jose L (Tutor)

[00:06:00] cube root of 8 = ?

Guest (Customer)

[00:06:05] 2

Jose L (Tutor)

[00:06:25] what happens to y

[00:06:31] when x gets more positive

[00:06:40] for example x=1, then 10, then 100....

Guest (Customer)

[00:06:57] it increases

Jose L (Tutor)

[00:07:15] how about then x gets more negative

[00:07:20] hint: look at x^2

[00:07:31] so using x=-1, then -10, then -100...ect

[00:07:33] etc

[00:07:58] for example (-1)^2 then (-10)^2...

Guest (Customer)

[00:08:04] still increases

Jose L (Tutor)

[00:08:05] yes

[00:08:13] the same as x=1, 10, and so on

Guest (Customer)

[00:08:22] ok

Jose L (Tutor)

[00:08:23] so looking at the graph

[00:08:25] the range is what?

[00:08:30] look at the y-axis

[00:08:35] that's the hint

Guest (Customer)

[00:08:54] [2, infinity)

Jose L (Tutor)

[00:08:59] yes

Guest (Customer)

[00:09:06] oh thank God

[00:09:08] lol

Jose L (Tutor)

[00:09:08] questions on that?

Guest (Customer)

[00:09:14] i think i get it now

Jose L (Tutor)

[00:09:23] yes it's tricky sometimes

[00:09:30] just need to practice different problems

[00:09:34] to get used to it

[00:10:05] any questions?

Guest (Customer)

[00:10:06] yeah. i will
so i have to
graph? to figure out the range?

Jose L (Tutor)

[00:10:15] well you don't have to graph

[00:10:21] you can also make a table

[00:10:32] and another way is

[00:10:47] the domain of f(x)....is the range of inverse f(x)

[00:10:56] wait let me see

[00:11:55] yes

Guest (Customer)

[00:12:15] oh yay! i like tht better haha

Jose L (Tutor)

[00:12:23] yep so there are some methods

[00:12:31] in case you get stuck using one method

[00:12:34] try another

Guest (Customer)

[00:12:43] ok thank you so much Jose!

Jose L (Tutor)

[00:12:48] sure

[00:12:50]

[00:12:53] Thank you for using the service!
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Guest (Customer)

[00:12:55] bye