Question

Maximal domain of g(x)...

g(x) = (3) - (4/(x+2))

Is it x + 2 = 0..
x = - 2...
Is that how we get the maximal domain??

Answer 1

The maximal domain is the set of all x that allows your function to exist.

Answer 2

So here, your function is not defined at the point x=-2 since there, the denominator is 0.

Answer 3

so it can't equal to zero because it's over something

Answer 4

oh okay thanks

Answer 5

So your domain is the set of all x real except for x=0.

Answer 6

i think real, as long as X not equal to 0

Answer 7

x+2 not equal to zero

Answer 8

so is the answer...? R / -2 ?

Answer 9

yes

Answer 10

\[\mathbb{R} - \left\{ -2 \right\}\]

Answer 11

Thanks :)

Answer 12

np

Answer 13

Also what is it's range? + it wants the inverse...

Answer 14

is the range infinity to 3 ?

Answer 15

negative infinity?

Answer 16

u want this (-infinity,2),( 2, infinity)? but i never see a form like that, u just write R-{-2}

Answer 17

Okay, do you know how to get the inverse?

Answer 18

You can use the definition for the inverse.

g is the inverse of f if
\[f(g(x))=x=g(f(x))\]

Answer 19

The inverse of your function can be found then as,\[f(g(x))=3-\frac{4}{g(x)+2}=x\]and solve for g(x).

Answer 20

do we put the w hole g(x) under that 4 ?

Answer 21

?

Answer 22

oh sorry.. do we re arrange the g(x) to the other side or something?

Answer 23

yeah, you solve for g(x)

Answer 24

4 = x (g(x)+2)

Answer 25

where'd you 3 go?

Answer 26

oh lol, -1 = x (g(x) + 2)

Answer 27

\[3-\frac{4}{g(x)+2}=x \rightarrow g(x)=\frac{4}{3-x}-2\]

Answer 28

check, i'm being distracted by different people

Answer 29

g(x) = 3- 4/x+2.... and inverse is 3 - 4/g(x) +2... can you just leave it like that?

Answer 30

y = 3- (4/x+2)
x = 3-(4/y+2)
and then simplify

Answer 31

Take your original function.
Put g(x) in place of x and replace f(x) with x
Solve (rearrange) so you have g(x) = blah blah

Answer 32

how to simplify after... -1 = x(g(x) + 2) ?

Answer 33

expand

Answer 34

x(g(x)+2) = xg(x) + 2x

Answer 35

subtract 2x from both sides

Answer 36

divide by x

Answer 37

but i think you've made a mistake

Answer 38

I'll write it out

Answer 39

it wants the inverse g^-1... of g(x) = (3) - (4/(x+2))

Answer 40

y = 3- (4/x+2)
x = 3-(4/y+2)
x(y+2) = 3-4
x(y+2)=-1
y+2 = -1/x
y = (-1/x) -2
can this make sense?

Answer 41

Yeah, same thing, different notation.

Answer 42

yeah it makes sense except the G^-1.... the inverse... it looks different.

Answer 43

y = g^-1(x)

Answer 44

I stuffed the g(x) calc. because I'm writing it out on this damn thing, but the procedure is correct

Answer 45

=) Okay so should I just replace the y's with g(x).. as the answer?

Answer 46

You should end up with\[g^{-1}(x)=2\frac{x-1}{3-x}\]

Answer 47

no no ... don't just replace the y's with g(x)...

Do what I said...

Take your original function.
Put g^-1(x) in place of x and replace f(x) with x
Solve (rearrange) so you have g(x) = blah blah

Answer 48

it looks difficult to do but okay :)

Answer 49

You know what, there's a lot of confusion here. I'm going to write it out and scan.

Answer 50

Thanks :D :D :D I'll wait

Answer 51

Lokisan are you still there?

Answer 52

yes

Answer 53

scanning

Answer 54

Ok alright

Answer 55

Ive reformatted my pc so ill down pdf reader now, thanks for the link.

Answer 56

ok

Answer 57

Lokisan, did you use the retro version of this site?

Answer 58

?

Answer 59

retro

Answer 60

Yes, there was another version to this site

Answer 61

That means you joined it after the changes have taken place

Answer 62

Well, I think the retro was better, as you could type there realtime

Answer 63

I mean, it was more like a black board, and we didn't have to wait for the whole typing to be over

Answer 64

oh

Answer 65

Further more we could erase typed things and we could also type inbetween others' typings

Answer 66

yeah, this is a pain, and i can't use this site on my phone - not practical

Answer 67

oh that's heaps better

Answer 68

Would you mind visiting this one
https://docs.google.com/document/d/1-_5IUkf1O4EFkBw-kDEZV1T8THk4lzrpmQEzVKtfHHo/edit?hl=en_GB#

Answer 69

I get this:

Google Docs has encountered a server error. If reloading the page doesn't help, please contact us.

To discuss this or other issues, visit the Google Docs Help forum. To see the list of known problems, go to the Google Docs Known Issues page

Answer 70

Just try it once again or try refreshing it

Answer 71

That makes sense now! :D Thanks a lot and nice hand writing :)

Answer 72

No probs

Answer 73

Fan me!

Answer 74

Okay, I'm a fan already :)

Answer 75

Good :)