Aizhalee
  • Aizhalee
ALGEBRA HELP PLEASE , find the domain of each function
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Aizhalee
  • Aizhalee
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Aizhalee
  • Aizhalee
@mathmate
Aizhalee
  • Aizhalee
thank you tkhunny for coming by to help me

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tkhunny
  • tkhunny
Please stop tagging people and start showing your work. When is the denominator zero?
Aizhalee
  • Aizhalee
due to division it has to zero
Aizhalee
  • Aizhalee
f/g = 0
tkhunny
  • tkhunny
Wherever the denominator is zero, we have a place that is NOT in the Domain. Where is that?
Aizhalee
  • Aizhalee
by setting each factor as zero ? to find x
tkhunny
  • tkhunny
There you go. Factor it?
Aizhalee
  • Aizhalee
sorry I meant setting each factor EQUAL-ing to "0" x+1 = 0, x-12= 0. Am I right ? @tkhunny
tkhunny
  • tkhunny
\(x^{2} + x - 12 = 0\) Factor that. It's not 12 and 1.
Aizhalee
  • Aizhalee
OK (x+12) (x-1) ? Im sorry im just going by the way I have the notes in my notebook .
Aizhalee
  • Aizhalee
Thanks a lot Jim
jim_thompson5910
  • jim_thompson5910
|dw:1447029604790:dw|
Aizhalee
  • Aizhalee
Yes I have that written down :) but how can I factor it correctly please
jim_thompson5910
  • jim_thompson5910
there is really a 1 in front of the x terms (if there aren't coefficients there already) |dw:1447029675705:dw|
Aizhalee
  • Aizhalee
yes sir
jim_thompson5910
  • jim_thompson5910
|dw:1447029696452:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1447029753364:dw|
jim_thompson5910
  • jim_thompson5910
are you able to think of those two numbers?
Aizhalee
  • Aizhalee
6*-6 =-12
jim_thompson5910
  • jim_thompson5910
6 times -6 is not -12
Aizhalee
  • Aizhalee
my mistake 6*-2 =-12. I was thinking of additions >.<
jim_thompson5910
  • jim_thompson5910
that is true but 6 plus -2 does not equal +1 like we want
jim_thompson5910
  • jim_thompson5910
try another pair of factors
Aizhalee
  • Aizhalee
hmm ok 3*-4 ? or -1*12
jim_thompson5910
  • jim_thompson5910
3*-4 is very close notice how 3 plus -4 = -1 but we want +1
Aizhalee
  • Aizhalee
yikes , ok um 2 + -1 = 1
jim_thompson5910
  • jim_thompson5910
you were on the right track, just you had to flip the signs why not -3 and +4 ? -3 times 4 = -12 -3 + 4 = +1 so `x^2 + x - 12` factors to `(x-3)(x+4)` notice how the numbers -3 and 4 are part of the factorization like that
Aizhalee
  • Aizhalee
wow , Im sorry . and yes I do notice . thank you for explaining
jim_thompson5910
  • jim_thompson5910
so `x^2 + x - 12=0` turns into `(x-3)(x+4)=0` what are the two values of x that make this equation true?
Aizhalee
  • Aizhalee
if (0)(7)=0
jim_thompson5910
  • jim_thompson5910
what did you replace x with to get that?
Aizhalee
  • Aizhalee
zeros oriel
Aizhalee
  • Aizhalee
huh?
jim_thompson5910
  • jim_thompson5910
how did you go from `(x-3)(x+4)=0` to `(0)(7)=0` ?
Aizhalee
  • Aizhalee
to add 3 to x
jim_thompson5910
  • jim_thompson5910
you replaced x with 3, so that shows that x = 3 is one solution
jim_thompson5910
  • jim_thompson5910
what is the other solution
Aizhalee
  • Aizhalee
3 honestly brcause 3-3 = 0 and 3+4=7
jim_thompson5910
  • jim_thompson5910
yes and because 0 times any number is 0
jim_thompson5910
  • jim_thompson5910
to get the other solution, solve x+4 = 0 for x
Aizhalee
  • Aizhalee
dont use x= 3 ?
jim_thompson5910
  • jim_thompson5910
no you already used that
jim_thompson5910
  • jim_thompson5910
you can subtract 4 from both sides of `x+4 = 0` to solve for x
Aizhalee
  • Aizhalee
x=-6
jim_thompson5910
  • jim_thompson5910
nope
Aizhalee
  • Aizhalee
6
jim_thompson5910
  • jim_thompson5910
|dw:1447030607285:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1447030623935:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1447030645137:dw|
jim_thompson5910
  • jim_thompson5910
so hopefully you see that if `x+4 = 0` then `x = -4`
Aizhalee
  • Aizhalee
really? so 0-4 is -4 ?
jim_thompson5910
  • jim_thompson5910
yes
Aizhalee
  • Aizhalee
i thought the 0 would turn into 10 . but ok thank you for explaining jim
jim_thompson5910
  • jim_thompson5910
think of it like you're starting at 0 on the number line, then you move 4 spots to the left to end up at -4
jim_thompson5910
  • jim_thompson5910
The solutions to `x^2 + x - 12=0` are `x = 3 or x = -4`
jim_thompson5910
  • jim_thompson5910
the values `x = 3` and `x = -4` are the values that make the denominator zero, so you have to kick those values out of the domain the domain would be the set of all real numbers BUT x cannot equal 3 or it cannot equal -4 (to avoid division by zero errors)
Aizhalee
  • Aizhalee
Ohhh. I get it now .Thank you so much Jim I am adding this in my nitebook .
jim_thompson5910
  • jim_thompson5910
np
Aizhalee
  • Aizhalee
Bye take care God bless :)

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