Babynini
  • Babynini
f(x)= x/(1+x) g(x) = sin2x Find the following (along with their domains) a) fog b) gof c)fof d) gog
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Babynini
  • Babynini
@jim_thompson5910 help please!
Babynini
  • Babynini
a) fog f(g(x)) = f(sin2x)=sin2(1/(1+x))
zepdrix
  • zepdrix
Hmm that fog looks a little mixed up :d

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zepdrix
  • zepdrix
\[\large\rm f(\color{orangered}{x})=\frac{\color{orangered}{x}}{1+\color{orangered}{x}}\]Becomes:\[\large\rm f(\color{orangered}{g(x)})=\frac{\color{orangered}{\sin2x}}{1+\color{orangered}{\sin2x}}\]Ya? :o
zepdrix
  • zepdrix
What 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
  • Babynini
Just a second, trying to work it out on paper :)
Babynini
  • Babynini
haha yeah I wrote it correctly on paper but did it wrong on here xD sorry! just a moment.
zepdrix
  • zepdrix
:3
zepdrix
  • zepdrix
For part A, do you understand how to find the domain of the composition?
Babynini
  • Babynini
I am only having issues with the domain for c now. The rest are all entered and correct.
Babynini
  • Babynini
c) x/1+2x Domain: (-infinity, -1/2) union (-1/2, infinity) it keeps saying the domain is wrong?
zepdrix
  • zepdrix
Oh sorry I ran off for a sec >.<
Babynini
  • Babynini
You're all good :)
zepdrix
  • zepdrix
Hmm, I forget how these compositions work sometimes. I guess we need to carry this information around with us before simplifying,\[\large\rm f(x)=\frac{x}{1+x},\qquad\qquad x\ne-1\]So when we get to this composition we have,\[\large\rm f(f(x))=\frac{x}{1+2x},\qquad\qquad x\ne-1,-\frac{1}{2}\]Try that maybe? :o
Babynini
  • Babynini
aaaah. so in interval notation it would be: (-infinity, -1) union (-1,-1/2)union(-1/2, infinity)
zepdrix
  • zepdrix
Mmmmm yah I think so :)
zepdrix
  • zepdrix
|dw:1443246434171:dw|
Babynini
  • Babynini
Yaay! 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
  • zepdrix
Yah, that's kinda tricky! :)
Babynini
  • Babynini
You and your gorgeous drawings xP thanks. That makes sense.
zepdrix
  • zepdrix
XD
zepdrix
  • zepdrix
need moar light bulbs ...... to bury
Babynini
  • Babynini
hahah we'll see.
DanJS
  • DanJS
domain 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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