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 2 years ago
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
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

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AndreaYoung1
 2 years ago
Best ResponseYou've already chosen the best response.0Have you searched the web? I havn't studied this yet /:

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

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

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

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.1f(x) + g(x) literally means "add the functions f(x) and g(x)"

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

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.1that'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?

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.1yeah it seems too simple that it looks like a trick question, but it's not

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

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

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

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

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

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

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

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.1the domain is the same because the radicands (the stuff in the square roots) are the same

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

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

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

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.1the first part is correct, but the domain will be slightly different

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.1now 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)

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

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

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

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

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.1well it's with different numbers, I just wanted to know the difference.

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

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

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

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

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

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.1oh my bad, there should be a closing parenthesis after g(x)

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.1but everything else is correct

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

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

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

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

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.19x +1 = 0 x = ???

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

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

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.1start 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)

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

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

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

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

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

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

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.1then to find the domain would I do x+1=0 x=1?

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

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

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.1so how would you do that domain then? would it be.. x cannot be zero?

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

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

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.11/(1/x) = (1/1)/(1/x) 1/(1/x) = (1/1)*(x/1) 1/(1/x) = x/1 1/(1/x) = x

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

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

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

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

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

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

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

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

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

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.11) what is g(2)??

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

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

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

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

monroe17
 2 years ago
Best ResponseYou've already chosen the best response.1so what would be the corresponding function value? how do I put that together?

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

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

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

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.1this example may be a bit confusing with all the 2's...

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.1but 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

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

jim_thompson5910
 2 years ago
Best ResponseYou've already chosen the best response.1close g(0) = 1 f(g(0)) = f(1) f(g(0)) = 1
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