anonymous
  • anonymous
what is the domain and range of
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
|dw:1378135135335:dw|
terenzreignz
  • terenzreignz
When you have rational expressions, the only thing you need to make sure of is that the denominator does not become zero. Here, you only have a rational expression, so the domain is all real numbers except that value of x which would make x - 3 = 0
anonymous
  • anonymous
ah.. so the domain is all real numbers except 3? :)

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More answers

terenzreignz
  • terenzreignz
That's correct.
terenzreignz
  • terenzreignz
Range is tricky, but first, I want you to factor the numerator. And tell me what follows...
anonymous
  • anonymous
x^2-9/ x-3 = (x-3)(x+3) / x-3
terenzreignz
  • terenzreignz
Cancel out...
anonymous
  • anonymous
x+3 ..
anonymous
  • anonymous
eh, how to get the range? :)
terenzreignz
  • terenzreignz
Sorry.... Okay, so, your function is basically (though not really) just x + 3 Which can take any value, right?
terenzreignz
  • terenzreignz
I mean, for any real number, there is another real number x such that x+3 is that number.
anonymous
  • anonymous
ah..? then?
terenzreignz
  • terenzreignz
Then it really should be all-real numbers...
terenzreignz
  • terenzreignz
but...?
terenzreignz
  • terenzreignz
But what? Come on, give it a bit of thought... there is ONE value that is not in the range.. one value that the function may never be equal to...
anonymous
  • anonymous
except 6.. but why 6?
terenzreignz
  • terenzreignz
Because for x+3 to be equal to 6... x has to be 3. And 3... is not in the domain :P (IE, x was never allowed to take the value, 3)
anonymous
  • anonymous
what is IE? :)
terenzreignz
  • terenzreignz
Id est. It's a Latin phrase meaning "that is to say..."
terenzreignz
  • terenzreignz
duh ^_^ lol jk
anonymous
  • anonymous
ah. :) okay.. :) .. can you give me some example of that? :)
terenzreignz
  • terenzreignz
Example of what? Latin phrases?
anonymous
  • anonymous
no... example of finding the domain and range na ganun din.. hehe :)
terenzreignz
  • terenzreignz
Isa lang ah. Inaantok na ako. Find the domain of \[\Large \frac{x^3-8}{x^2-4}\]
anonymous
  • anonymous
ang hirap naman ..
terenzreignz
  • terenzreignz
oo nga eh domain lang naman eh. Anong mga value ng x ang magpapa-zero sa denominator?
anonymous
  • anonymous
2 and -2?
terenzreignz
  • terenzreignz
yun lang... so ano yung domain?
anonymous
  • anonymous
haha.. di ko alam .. amp, ang domain ay all real numbers except 2 and -2?
terenzreignz
  • terenzreignz
iyan. Kaya mo naman pala eh :P
anonymous
  • anonymous
yehey! haha.. eh ang range pano?
terenzreignz
  • terenzreignz
ewan... medyo mahirap. kaya nga domain lang tinanong ko, di ba? :P
anonymous
  • anonymous
ayy.. ngek? haha.. okay.. ito pa, pde? pano to'? ln(lne^e^200) ?
terenzreignz
  • terenzreignz
Oh... sandali ah... Tandaan mo ito: \[\Large \ln e^x= x\]
terenzreignz
  • terenzreignz
\[\huge \ln e^{\color{red}{e^{200}}}=\color{red}?\]
anonymous
  • anonymous
ln 200 ?
anonymous
  • anonymous
ay ndi pla.. 200 lng pla?
terenzreignz
  • terenzreignz
yup. Yan na yun.
anonymous
  • anonymous
alin ang sagot: ln 200 o 200 lang?
terenzreignz
  • terenzreignz
alin kaya? Wag mo kasing madaliin -.-
terenzreignz
  • terenzreignz
Oh... \[\Large \ln e^{\color{red}x}=\color{red}x \] Ito guide mo...
terenzreignz
  • terenzreignz
Ano ngayon ito? \[\huge \ln e^{\color{red}{e^{200}}}=\color{red}?\]
anonymous
  • anonymous
ang ln e ay 1 . tapos yung e^200 ay 200 lang.. dahil parang ibababa lang yung 200, tama ba? :)
terenzreignz
  • terenzreignz
-.- Sandali lang ah... sabihin muna nating \[\Large \color{blue}p = \color{red}{e^{200}}\]
terenzreignz
  • terenzreignz
Para hindi ka nalilito...
anonymous
  • anonymous
oo. tapos?
terenzreignz
  • terenzreignz
-.- \[\Large \ln e^{e^{200}}= \ln e^\color{blue}{p}\]
terenzreignz
  • terenzreignz
Ano ito ngayon?
anonymous
  • anonymous
yung e^200 ?
terenzreignz
  • terenzreignz
Okay! So... \[\Large \ln e^{e^{200}}=e^{200}\] Tapos ito, ano naman ang ln nito?
anonymous
  • anonymous
ln 200 .
terenzreignz
  • terenzreignz
\[\Large \ln e^{200}= \ln 200 \qquad \color{red}{?????}\] \[\Huge \color{red}{No!!!!!}\]
anonymous
  • anonymous
sorry.. 200 lang pla..
terenzreignz
  • terenzreignz
>.> Wag kalilimutan ang basics!!!! inaantok na ako... matulog ka na nga rin... <.< lagpas 12:00 na eh... -.-
anonymous
  • anonymous
oo.. hindi na. tatandaan ko na.. salamat ^_^ . gege. tulog na ikaw.. ako'y mamaya pang 2 ata.. salamat ulit. :) :D galing mo talaga.. ^_^ hehe

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