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??

- anonymous

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- anonymous

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

- anonymous

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

- anonymous

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

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## More answers

- anonymous

oh okay thanks

- anonymous

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

- anonymous

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

- anonymous

x+2 not equal to zero

- anonymous

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

- anonymous

yes

- anonymous

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

- anonymous

Thanks :)

- anonymous

np

- anonymous

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

- anonymous

is the range infinity to 3 ?

- anonymous

negative infinity?

- anonymous

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

- anonymous

Okay, do you know how to get the inverse?

- anonymous

You can use the definition for the inverse.
g is the inverse of f if
\[f(g(x))=x=g(f(x))\]

- anonymous

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).

- anonymous

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

- anonymous

?

- anonymous

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

- anonymous

yeah, you solve for g(x)

- anonymous

4 = x (g(x)+2)

- anonymous

where'd you 3 go?

- anonymous

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

- anonymous

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

- anonymous

check, i'm being distracted by different people

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

expand

- anonymous

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

- anonymous

subtract 2x from both sides

- anonymous

divide by x

- anonymous

but i think you've made a mistake

- anonymous

I'll write it out

- anonymous

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

- anonymous

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?

- anonymous

Yeah, same thing, different notation.

- anonymous

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

- anonymous

y = g^-1(x)

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

it looks difficult to do but okay :)

- anonymous

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

- anonymous

Thanks :D :D :D I'll wait

- anonymous

Lokisan are you still there?

- anonymous

yes

- anonymous

scanning

- anonymous

Ok alright

- anonymous

##### 1 Attachment

- anonymous

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

- anonymous

ok

- anonymous

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

- anonymous

?

- anonymous

retro

- anonymous

Yes, there was another version to this site

- anonymous

That means you joined it after the changes have taken place

- anonymous

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

- anonymous

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

- anonymous

oh

- anonymous

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

- anonymous

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

- anonymous

oh that's heaps better

- anonymous

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

- anonymous

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

- anonymous

Just try it once again or try refreshing it

- anonymous

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

- anonymous

No probs

- anonymous

Fan me!

- anonymous

Okay, I'm a fan already :)

- anonymous

Good :)

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