The domain of a composition of two functions

Question

osanseviero · Answer

Natural domain of
$$f(x)=\frac{ 1 }{ x-3 }$$
g(x)=5x

$$(Fog)(x)$$

It is x$$x \in[-1,infinite)$$ ?

hartnn · Answer

what did you get for f(g(x)) = .... ?

osanseviero · Answer

Let me do it, give me a sec

hartnn · Answer

sure, take your time :)

osanseviero · Answer

$$\sqrt{2-4x}$$

osanseviero · Answer

ooops sorry, confused question, give me another sec

hartnn · Answer

am i reading the question correct ?
f(x) =1/ (x-3)
g(x) =5x 
?
i don't see .....
oh, okk

osanseviero · Answer

Sorry, the mistake was the question

osanseviero · Answer

$$f(x)=\sqrt{x+1}$$
g(x)=1-4x

hartnn · Answer

yes, f(g(x)) is correct then

hartnn · Answer

now quantity under square root cannot be negative

osanseviero · Answer

So the domain is x<= 1/2 for the square root, and I take the intersection

osanseviero · Answer

[-1,1/2]

hartnn · Answer

yep, thats correct! good :)

osanseviero · Answer

So I need to take the domain of FoG with
$$\left\{ x \in Dg|g(x)\in Df \right\}$$

osanseviero · Answer

And intersect that with the domain of the last result?

hartnn · Answer

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 · Answer

Perfect, thanks

hartnn · Answer

welcome ^_^