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monroe17
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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
 2 years ago
 2 years 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
 2 years ago
 2 years 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 /:
 2 years ago

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

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

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

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

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

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

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

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

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

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
yes
 2 years ago

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

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

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

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

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

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

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

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

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

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

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
dw:1346027228896:dw
 2 years 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)
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
but everything else is correct
 2 years 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)?
 2 years ago

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

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

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

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

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

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

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

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

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
yes
 2 years ago

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

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

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

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

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
the 1 isn't part of the fraction
 2 years 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?
 2 years ago

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

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

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

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
yes
 2 years 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?
 2 years ago

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

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

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

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

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
yes
 2 years ago

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

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

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
perfect
 2 years ago

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

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

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

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

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

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

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

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

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
what's that
 2 years 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))
 2 years ago

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

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

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

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

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

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

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

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

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

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

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