osanseviero
  • osanseviero
The domain of a composition of two functions
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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osanseviero
  • osanseviero
Natural domain of \[f(x)=\frac{ 1 }{ x-3 }\] g(x)=5x \[(Fog)(x)\] It is x\[x \in[-1,infinite)\] ?
hartnn
  • hartnn
what did you get for f(g(x)) = .... ?
osanseviero
  • osanseviero
Let me do it, give me a sec

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hartnn
  • hartnn
sure, take your time :)
osanseviero
  • osanseviero
\[\sqrt{2-4x}\]
osanseviero
  • osanseviero
ooops sorry, confused question, give me another sec
hartnn
  • hartnn
am i reading the question correct ? f(x) =1/ (x-3) g(x) =5x ? i don't see ..... oh, okk
osanseviero
  • osanseviero
Sorry, the mistake was the question
osanseviero
  • osanseviero
\[f(x)=\sqrt{x+1}\] g(x)=1-4x
hartnn
  • hartnn
yes, f(g(x)) is correct then
hartnn
  • hartnn
now quantity under square root cannot be negative
osanseviero
  • osanseviero
So the domain is x<= 1/2 for the square root, and I take the intersection
osanseviero
  • osanseviero
[-1,1/2]
hartnn
  • hartnn
yep, thats correct! good :)
osanseviero
  • osanseviero
So I need to take the domain of FoG with \[\left\{ x \in Dg|g(x)\in Df \right\}\]
osanseviero
  • osanseviero
And intersect that with the domain of the last result?
hartnn
  • hartnn
i am not sure about what that notation says, but yes, you take the intersection domains of both the funtion with composite function to get the final domain
osanseviero
  • osanseviero
Perfect, thanks
hartnn
  • hartnn
welcome ^_^

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