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Babynini
 one year ago
f(x)= x/(1+x)
g(x) = sin2x
Find the following (along with their domains)
a) fog
b) gof
c)fof
d) gog
Babynini
 one year ago
f(x)= x/(1+x) g(x) = sin2x Find the following (along with their domains) a) fog b) gof c)fof d) gog

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Babynini
 one year ago
Best ResponseYou've already chosen the best response.0@jim_thompson5910 help please!

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0a) fog f(g(x)) = f(sin2x)=sin2(1/(1+x))

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3Hmm that fog looks a little mixed up :d

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3\[\large\rm f(\color{orangered}{x})=\frac{\color{orangered}{x}}{1+\color{orangered}{x}}\]Becomes:\[\large\rm f(\color{orangered}{g(x)})=\frac{\color{orangered}{\sin2x}}{1+\color{orangered}{\sin2x}}\]Ya? :o

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3What you posted: \(\large\rm sin\left(2\color{orangered}{\frac{1}{1+x}}\right)\) This is actually the function f being plugged into g, \[\large\rm \sin\left(2\color{orangered}{\frac{1}{1+x}}\right)=\sin\left(2\color{orangered}{f(x)}\right)=g(\color{orangered}{f(x)})\]Where,\[\large\rm \sin(2\color{orangered}{x})=g(\color{orangered}{x})\]

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0Just a second, trying to work it out on paper :)

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0haha yeah I wrote it correctly on paper but did it wrong on here xD sorry! just a moment.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3For part A, do you understand how to find the domain of the composition?

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0I am only having issues with the domain for c now. The rest are all entered and correct.

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0c) x/1+2x Domain: (infinity, 1/2) union (1/2, infinity) it keeps saying the domain is wrong?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3Oh sorry I ran off for a sec >.<

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3Hmm, I forget how these compositions work sometimes. I guess we need to carry this information around with us before simplifying,\[\large\rm f(x)=\frac{x}{1+x},\qquad\qquad x\ne1\]So when we get to this composition we have,\[\large\rm f(f(x))=\frac{x}{1+2x},\qquad\qquad x\ne1,\frac{1}{2}\]Try that maybe? :o

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0aaaah. so in interval notation it would be: (infinity, 1) union (1,1/2)union(1/2, infinity)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3Mmmmm yah I think so :)

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0Yaay! That is correct. Finally! Thank you so much :D I hadn't thought of that. So it is important to keep in mind the domains for the original functions

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3Yah, that's kinda tricky! :)

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0You and your gorgeous drawings xP thanks. That makes sense.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.3need moar light bulbs ...... to bury

DanJS
 one year ago
Best ResponseYou've already chosen the best response.0domain of nested functions like that is the intersection of each domain, for f(g(x)) , domain of g and domain of f of g.
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