osanseviero
The domain of a composition of two functions
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osanseviero
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Natural domain of
\[f(x)=\frac{ 1 }{ x-3 }\]
g(x)=5x
\[(Fog)(x)\]
It is x\[x \in[-1,infinite)\] ?
hartnn
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what did you get for f(g(x)) = .... ?
osanseviero
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Let me do it, give me a sec
hartnn
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sure, take your time :)
osanseviero
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\[\sqrt{2-4x}\]
osanseviero
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ooops sorry, confused question, give me another sec
hartnn
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am i reading the question correct ?
f(x) =1/ (x-3)
g(x) =5x
?
i don't see .....
oh, okk
osanseviero
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Sorry, the mistake was the question
osanseviero
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\[f(x)=\sqrt{x+1}\]
g(x)=1-4x
hartnn
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yes, f(g(x)) is correct then
hartnn
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now quantity under square root cannot be negative
osanseviero
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So the domain is x<= 1/2 for the square root, and I take the intersection
osanseviero
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[-1,1/2]
hartnn
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yep, thats correct! good :)
osanseviero
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So I need to take the domain of FoG with
\[\left\{ x \in Dg|g(x)\in Df \right\}\]
osanseviero
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And intersect that with the domain of the last result?
hartnn
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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
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Perfect, thanks
hartnn
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welcome ^_^