## Babynini one year ago f(x)= x/(1+x) g(x) = sin2x Find the following (along with their domains) a) fog b) gof c)fof d) gog

1. Babynini

2. Babynini

a) fog f(g(x)) = f(sin2x)=sin2(1/(1+x))

3. zepdrix

Hmm that fog looks a little mixed up :d

4. 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

5. 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,$\large\rm \sin(2\color{orangered}{x})=g(\color{orangered}{x})$

6. Babynini

Just a second, trying to work it out on paper :)

7. Babynini

haha yeah I wrote it correctly on paper but did it wrong on here xD sorry! just a moment.

8. zepdrix

:3

9. zepdrix

For part A, do you understand how to find the domain of the composition?

10. Babynini

I am only having issues with the domain for c now. The rest are all entered and correct.

11. Babynini

c) x/1+2x Domain: (-infinity, -1/2) union (-1/2, infinity) it keeps saying the domain is wrong?

12. zepdrix

Oh sorry I ran off for a sec >.<

13. Babynini

You're all good :)

14. 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

15. Babynini

aaaah. so in interval notation it would be: (-infinity, -1) union (-1,-1/2)union(-1/2, infinity)

16. zepdrix

Mmmmm yah I think so :)

17. zepdrix

|dw:1443246434171:dw|

18. 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

19. zepdrix

Yah, that's kinda tricky! :)

20. Babynini

You and your gorgeous drawings xP thanks. That makes sense.

21. zepdrix

XD

22. zepdrix

need moar light bulbs ...... to bury

23. Babynini

hahah we'll see.

24. 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.