A community for students.
Here's the question you clicked on:
 0 viewing
monroe17
 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
monroe17
 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

This Question is Closed

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
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.