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

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

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

oh okay thanks

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

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

x+2 not equal to zero

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

yes

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

Thanks :)

np

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

is the range infinity to 3 ?

negative infinity?

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

Okay, do you know how to get the inverse?

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

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

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

yeah, you solve for g(x)

4 = x (g(x)+2)

where'd you 3 go?

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

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

check, i'm being distracted by different people

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

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

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

expand

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

subtract 2x from both sides

divide by x

but i think you've made a mistake

I'll write it out

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

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?

Yeah, same thing, different notation.

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

y = g^-1(x)

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

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

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

it looks difficult to do but okay :)

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

Thanks :D :D :D I'll wait

Lokisan are you still there?

yes

scanning

Ok alright

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

ok

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

retro

Yes, there was another version to this site

That means you joined it after the changes have taken place

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

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

oh

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

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

oh that's heaps better

Just try it once again or try refreshing it

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

No probs

Fan me!

Okay, I'm a fan already :)

Good :)