Composition Functions: Finding f(g(x)) for F(x)=1/(1+x) and G(x)=1/(2+x)

[Coco12]

Homework Statement

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

Homework Equations

No equations for composition functions

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?

 

[tiny-tim]

Hi Coco12!

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?

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.

 

[Coco12]

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.

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

 

[tiny-tim]

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

(what is it with you and brackets? )

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

anyway, what did you get?​

 

[Coco12]

Never mind I got it. Thank you

 

[Student100]

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

This would be why -1 is forbidden.

 

[Coco12]

where did you get (1+x)??

 

[tiny-tim]

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

This would be why -1 is forbidden.

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

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

 

[Student100]

where did you get (1+x)??

1. Homework Statement

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

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.

 

[Coco12]

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

Look at the above video

 

[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. :)

 

[Coco12]

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

 

[Student100]

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

 

[Mark44]

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

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.

 

[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