Homework Help: Composition functions

1. Dec 13, 2013

Coco12

1. The problem statement, all variables and given/known data

If F(x)= 1/(1+x)
G(x)= 1/(2+x)
determine f(g(x))

2. Relevant equations

No equations for composition functions

3. The attempt at a solution
F(g(x)) = 1/1+ 1/(2+x)

Then do you try to eliminate the fraction in the denominator by multiplying it by (2+x)?

They said that the x values that would not work are -3,-2,-1. I understand where they got -3 and -2 but where did they get -1?

2. Dec 13, 2013

tiny-tim

Hi Coco12!
Let's see … you got 1/(1+ 1/(2+x))

(pleeease use more brackets … you confused me at first )

= 1/((3+x)/(2+x))

= (2+x)/(3+x) which is not defined if x = -3
(and G(x) was not defined anyway at x = -2 )

Yes i agree , i don't see why x = -1 is forbidden.

3. Dec 13, 2013

Coco12

Wait how did you get 1/(3+x)(2+x)??

4. Dec 13, 2013

tiny-tim

(what is it with you and brackets? )

i didn't, i got 1/((3+x)/(2+x))

anyway, what did you get?​

5. Dec 13, 2013

Coco12

Never mind I got it. Thank you

6. Dec 13, 2013

Student100

If F(x)= 1/(1+x)

This would be why -1 is forbidden.

7. Dec 13, 2013

Coco12

where did you get (1+x)??

8. Dec 13, 2013

tiny-tim

But we're not interested in F(x), only in F(G(x)),

and only G(x) = -1 is forbidden (ie x = -3)

Last edited: Dec 13, 2013
9. Dec 13, 2013

Student100

Is this the problem? That's your f function. There is a thoerm that states the domains of both functions need to be considered in a compoistion. Unless I'm making this up in my head.

10. Dec 13, 2013

Coco12

I thought you only need to consider the domain of the inner function and the overall function.

Look at the above video

Last edited by a moderator: Sep 25, 2014
11. Dec 13, 2013

Student100

Yeah I just looked it up; I guess I was thinking about something else. Sorry for the confusion, I'll slump back to my little corner now. :)

Last edited: Dec 13, 2013
12. Dec 13, 2013

Coco12

no problem. Do you know anything about the in and out method of solving for the domain and ranges?

13. Dec 13, 2013

Student100

Never heard of it, I'm probably a bit rustier than I should be with all this.

14. Dec 13, 2013

Staff: Mentor

I haven't heard of it being called that, but for the composition f(g(x)), x has to be in the domain of g, and the range of g is the domain of f.

15. Dec 13, 2013

Coco12

I have another question related to that in the forums. Can you please see if you can help me? How do u find the domain and ranges of composition function