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monroe17
Group Title
Given that f(x)=sqrt{2 + x} and g(x)=sqrt{2  x}, find formulas for the following functions, and their domains. In each case, enter the domain using interval notation.
(a) f+g= and its domain is
 one year ago
 one year ago
monroe17 Group Title
Given that f(x)=sqrt{2 + x} and g(x)=sqrt{2  x}, find formulas for the following functions, and their domains. In each case, enter the domain using interval notation. (a) f+g= and its domain is
 one year ago
 one year ago

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AndreaYoung1 Group TitleBest ResponseYou've already chosen the best response.0
Have you searched the web? I havn't studied this yet /:
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
I have.. I can't find anything similar :/
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
@qpHalcy0n can you help me?
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
@jim_thompson5910 can you please help? :)
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
f(x) + g(x) literally means "add the functions f(x) and g(x)"
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
but since f(x) = sqrt(2+x) and g(x) = sqrt(2x), we know that f(x) + g(x) = sqrt(2+x) + sqrt(2x)
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
that's what I got.. But, I wasn't sure if f(x) + g(x) = sqrt(2+x) + sqrt(2x) was correct or not.. how would I find the domain?
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
yeah it seems too simple that it looks like a trick question, but it's not
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
the domain is the set of allowable inputs, or x values
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
remember that you can't take the square root of a negative number, so 2+x >= 0 and 2x >= 0
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
those two inequalities become x >= 2 and x <= 2 which combine to 2 <= x <= 2
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
so, in interval notation.. it would be (inf,2)U(2,inf) ?
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
no, [2, 2]
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
that represents \(\Large 2 \le x \le 2\)
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
oh okay... and would this be correct? f(x)  g(x) = sqrt(2+x)  sqrt(2x)
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
yes that's 100% correct
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
the domain is the same because the radicands (the stuff in the square roots) are the same
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
f(x) * g(x) = sqrt(2+x) * sqrt(2x) ?
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
yes
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
domains are the same (for the same reason explained above)
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
domain is*
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
f(x)/g(x) = sqrt(2+x)/sqrt(2x) and same domain?
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
the first part is correct, but the domain will be slightly different
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
now we have to avoid dividing by zero, so 2x can't be zero 2x = 0 x = 2 so if x = 2, then 2x is zero. So we toss out x = 2 from the domain So the domain is now [2, 2)
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
so now what is the difference between f+g and fog(x)?
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
f+g means "add f and g" fog(x) means "start with f(x), and plug in g(x) as the input"
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
fog(x) is the same as f(g(x))
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
\[\Large f(x) = \sqrt{2+x}\] \[\Large f(g(x)) = \sqrt{2+g(x)}\] \[\Large f(g(x)) = \sqrt{2+\sqrt{2x}}\]
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
well it's with different numbers, I just wanted to know the difference.
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
i gotcha, do you see how I'm getting that?
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
f(g(x))=2+sqrt(2x)?
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
f(x) = sqrt(2+x) and g(x) = sqrt(2x) correct?
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
Then \[\Large f(g(x)) = \sqrt{2+\sqrt{2x}}\] or \[\Large f\circ g(x) = \sqrt{2+\sqrt{2x}}\]
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
can you draw that? cause its not showing up correct.,. and im a lil confused
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
dw:1346027228896:dw
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
oh my bad, there should be a closing parenthesis after g(x)
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
but everything else is correct
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
okay so if f(x)=1/x and g(x)= 9x+1 fog(x) would be... 1/(9x+1)?
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
yes perfect
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
and its domain would be all real numbers except ...?
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
what makes 9x+1 equal to zero?
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
anything less than zero?
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
9x +1 = 0 x = ???
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
good, so x can be any number but 1/9
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
[1/9,inf] ?
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
(inf, 1/9) U (1/9, inf)
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
start with (inf, inf), which is the entire number line then poke a hole at 1/9 to get (inf, 1/9) U (1/9, inf)
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
for the domain it it says.. its domain is all real numbers except __ so would I just put in 1/9?
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
yes
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
that's in a more understandable way (in my opinion)
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
interval notation can be a little tricky to grasp
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
haha ya! gof(x) would be 9(1/x)+1?
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
yes, which becomes 9/x + 1
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
the 1 isn't part of the fraction
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
then to find the domain would I do x+1=0 x=1?
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
no, the denominator is just x
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
\[\Large f \circ g(x) = \frac{9}{x}+1\]
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
oh its (9/x)+1?
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
yes
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
so how would you do that domain then? would it be.. x cannot be zero?
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
yes, x can be any number but 0
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
would fof(x) be 1/(1/x).. so 1?
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
1/(1/x) = (1/1)/(1/x) 1/(1/x) = (1/1)*(x/1) 1/(1/x) = x/1 1/(1/x) = x
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
So 1/(1/x) simplifies to x
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
We have to add the restriction that x can't be zero to make sure that the two expressions are completely equivalent
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
fof(x)=x and its domain is all real numbers except 0?
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
yes
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
you nailed it
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
gog(x)=9(9x+1)+1=81x+9+1=81x+10?
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
perfect
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
domain: all real numbers
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
since the result is a polynomial
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
it says... its domain is (__,__)
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
inf, inf?
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
yes it is
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
yyayyy! thank you!
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
you're welcome
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
one more thing :/ ?
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
what's that
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
How do I find the corresponding function values. 1. f(g(2)) 2. f(g(0))
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
1) what is g(2)??
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
that's the point at (2,2)?
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
look at g(x) and not f(x)
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
you are correct, the point (2,2) is on g(x)
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
so f(g(2)) = f(2)
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
so what would be the corresponding function value? how do I put that together?
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
cause I tried f(2) and f(1) for the next one and they're both wrong.
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
notice how (2,2) is on f(x)
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
so f(2) = 2
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
which means overall f(g(2)) = 2
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
this example may be a bit confusing with all the 2's...
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
but the idea is you start with g(x), plug in x = 2 then you get some result, which you plug into f(x) to get your answer
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
so for the second one.. f(g(0)) (0,1)?
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
close g(0) = 1 f(g(0)) = f(1) f(g(0)) = 1
 one year ago

monroe17 Group TitleBest ResponseYou've already chosen the best response.1
all right thank you!
 one year ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
sure thing
 one year ago
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