how do you find f o f if f(x)=1/x+1

Question

harsimran_hs4 · Answer

f o f (x) = f(f(x))
can you figure out now?

tabithax3 · Answer

@harsimran_hs4 i know it's $$f \left( \frac{ 1 }{ x+1 } \right)=\frac{ 1 }{ \frac{ 1 }{ x+1 }+1 } $$ but i don't know what to do after

dumbcow · Answer

simplify ... the easiest yet most difficult part :|

dumbcow · Answer

first combine denominator into single fraction

change 1 to (x+1)/(x+1)

tabithax3 · Answer

@dumbcow so it'll be $$\frac{ 1 }{x+1  }+\frac{ x+1 }{ x+1 }$$

dumbcow · Answer

yes

harsimran_hs4 · Answer

shouldn`t it be (x+1)/(x+2)

dumbcow · Answer

haha we're getting there

tabithax3 · Answer

@harsimran_hs4 can you explain for me please?

tabithax3 · Answer

@dumbcow i stopped there, and went blank. help? haha

dumbcow · Answer

what they posted is the final answer...keep going and you'l get there
combine the 2 fractions ... they have a common denominator

harsimran_hs4 · Answer

$$\frac{ 1 }{ \frac{ 1 }{ x + 1} + 1} = \frac{ x+1}{ (x + 1)   +1}$$

harsimran_hs4 · Answer

howz it now 
did you get hold of the final answer

tabithax3 · Answer

@harsimran_hs4 how did you get x+1 on the numerator?

tabithax3 · Answer

oh never mind! got it

tabithax3 · Answer

@harsimran_hs4 i got $$\frac{ x+1 }{ x+2 }$$

dumbcow · Answer

that was horrible explanation ... you skipped all the intermediate steps

harsimran_hs4 · Answer

cool !!

dumbcow · Answer

so @tabithax3 , you understand it now

harsimran_hs4 · Answer

finally you got it right!!!
@dumbcow  i didn`t wanted to go that deep because it would have been spoonfeeding then and i wanted that @tabithax3  should figure that out herself

tabithax3 · Answer

@dumbcow explain? and @harsimran_hs4 but yet my book says the answer should have been $$\frac{ x }{ 2x+1 }$$ where $$x \neq-1, -\frac{ 1 }{ 2 }$$

harsimran_hs4 · Answer

ok i get it well we were solving considering f(x) = 1/(1+x) but it was f(x) = (1/x) + 1 this gives the required answer

tabithax3 · Answer

i think i got it, thanks for the help!

tabithax3 · Answer

@harsimran_hs4 i feel stupid now, i wrote the problem wrong all along. oops...but i got the answer right though. sorry for the trouble, but honestly, you really helped me out, and now i understand what to do with the section i'm working on :)

harsimran_hs4 · Answer

happens!!!

harsimran_hs4 · Answer

Welcome