## osanseviero 3 years ago The domain of a composition of two functions

1. osanseviero

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

2. hartnn

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

3. osanseviero

Let me do it, give me a sec

4. hartnn

5. osanseviero

$\sqrt{2-4x}$

6. osanseviero

ooops sorry, confused question, give me another sec

7. hartnn

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

8. osanseviero

Sorry, the mistake was the question

9. osanseviero

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

10. hartnn

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

11. hartnn

now quantity under square root cannot be negative

12. osanseviero

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

13. osanseviero

[-1,1/2]

14. hartnn

yep, thats correct! good :)

15. osanseviero

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

16. osanseviero

And intersect that with the domain of the last result?

17. 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

18. osanseviero

Perfect, thanks

19. hartnn

welcome ^_^