anonymous
  • anonymous
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??
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
The maximal domain is the set of all x that allows your function to exist.
anonymous
  • anonymous
So here, your function is not defined at the point x=-2 since there, the denominator is 0.
anonymous
  • anonymous
so it can't equal to zero because it's over something

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anonymous
  • anonymous
oh okay thanks
anonymous
  • anonymous
So your domain is the set of all x real except for x=0.
anonymous
  • anonymous
i think real, as long as X not equal to 0
anonymous
  • anonymous
x+2 not equal to zero
anonymous
  • anonymous
so is the answer...? R / -2 ?
anonymous
  • anonymous
yes
anonymous
  • anonymous
\[\mathbb{R} - \left\{ -2 \right\}\]
anonymous
  • anonymous
Thanks :)
anonymous
  • anonymous
np
anonymous
  • anonymous
Also what is it's range? + it wants the inverse...
anonymous
  • anonymous
is the range infinity to 3 ?
anonymous
  • anonymous
negative infinity?
anonymous
  • anonymous
u want this (-infinity,2),( 2, infinity)? but i never see a form like that, u just write R-{-2}
anonymous
  • anonymous
Okay, do you know how to get the inverse?
anonymous
  • anonymous
You can use the definition for the inverse. g is the inverse of f if \[f(g(x))=x=g(f(x))\]
anonymous
  • 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
  • anonymous
do we put the w hole g(x) under that 4 ?
anonymous
  • anonymous
?
anonymous
  • anonymous
oh sorry.. do we re arrange the g(x) to the other side or something?
anonymous
  • anonymous
yeah, you solve for g(x)
anonymous
  • anonymous
4 = x (g(x)+2)
anonymous
  • anonymous
where'd you 3 go?
anonymous
  • anonymous
oh lol, -1 = x (g(x) + 2)
anonymous
  • anonymous
\[3-\frac{4}{g(x)+2}=x \rightarrow g(x)=\frac{4}{3-x}-2\]
anonymous
  • anonymous
check, i'm being distracted by different people
anonymous
  • anonymous
g(x) = 3- 4/x+2.... and inverse is 3 - 4/g(x) +2... can you just leave it like that?
anonymous
  • anonymous
y = 3- (4/x+2) x = 3-(4/y+2) and then simplify
anonymous
  • 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
  • anonymous
how to simplify after... -1 = x(g(x) + 2) ?
anonymous
  • anonymous
expand
anonymous
  • anonymous
x(g(x)+2) = xg(x) + 2x
anonymous
  • anonymous
subtract 2x from both sides
anonymous
  • anonymous
divide by x
anonymous
  • anonymous
but i think you've made a mistake
anonymous
  • anonymous
I'll write it out
anonymous
  • anonymous
it wants the inverse g^-1... of g(x) = (3) - (4/(x+2))
anonymous
  • 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
  • anonymous
Yeah, same thing, different notation.
anonymous
  • anonymous
yeah it makes sense except the G^-1.... the inverse... it looks different.
anonymous
  • anonymous
y = g^-1(x)
anonymous
  • anonymous
I stuffed the g(x) calc. because I'm writing it out on this damn thing, but the procedure is correct
anonymous
  • anonymous
=) Okay so should I just replace the y's with g(x).. as the answer?
anonymous
  • anonymous
You should end up with\[g^{-1}(x)=2\frac{x-1}{3-x}\]
anonymous
  • 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
  • anonymous
it looks difficult to do but okay :)
anonymous
  • anonymous
You know what, there's a lot of confusion here. I'm going to write it out and scan.
anonymous
  • anonymous
Thanks :D :D :D I'll wait
anonymous
  • anonymous
Lokisan are you still there?
anonymous
  • anonymous
yes
anonymous
  • anonymous
scanning
anonymous
  • anonymous
Ok alright
anonymous
  • anonymous
anonymous
  • anonymous
Ive reformatted my pc so ill down pdf reader now, thanks for the link.
anonymous
  • anonymous
ok
anonymous
  • anonymous
Lokisan, did you use the retro version of this site?
anonymous
  • anonymous
?
anonymous
  • anonymous
retro
anonymous
  • anonymous
Yes, there was another version to this site
anonymous
  • anonymous
That means you joined it after the changes have taken place
anonymous
  • anonymous
Well, I think the retro was better, as you could type there realtime
anonymous
  • 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
  • anonymous
oh
anonymous
  • anonymous
Further more we could erase typed things and we could also type inbetween others' typings
anonymous
  • anonymous
yeah, this is a pain, and i can't use this site on my phone - not practical
anonymous
  • anonymous
oh that's heaps better
anonymous
  • anonymous
Would you mind visiting this one https://docs.google.com/document/d/1-_5IUkf1O4EFkBw-kDEZV1T8THk4lzrpmQEzVKtfHHo/edit?hl=en_GB#
anonymous
  • 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
  • anonymous
Just try it once again or try refreshing it
anonymous
  • anonymous
That makes sense now! :D Thanks a lot and nice hand writing :)
anonymous
  • anonymous
No probs
anonymous
  • anonymous
Fan me!
anonymous
  • anonymous
Okay, I'm a fan already :)
anonymous
  • anonymous
Good :)

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