## dtan5457 one year ago if f(g(x)=2x/(x+z), and g(x)=2x/(x+4) find f(x)

1. dtan5457

@jim_thompson5910

2. jim_thompson5910

is the x+z supposed to be x+4 ?

3. dtan5457

they are both under 2x so no

4. jim_thompson5910

then I'm not sure. That z is throwing me off

5. dtan5457

perhaps its an x+2? I mean my teacher's handwriting does look like a Z.

6. jim_thompson5910

that sounds possible

7. anonymous

i have an answer that might work, but i think you are supposed to use inverse functions some how

8. anonymous

by trial and error i came up with $f(x)=\frac{1}{x-\frac{2}{x}}$] we can see if that works, and also clean it up a bit

9. anonymous

in any case it is wrong, but i think i can fix it

10. anonymous

lets try this one $f(x)=\frac{1}{\frac{1}{x}-\frac{2}{2x}}$

11. anonymous

ok one more time without me being so stupid $f(x)=\frac{1}{\frac{1}{x}-\frac{2}{x+4}}$

12. Nnesha

*

13. anonymous

i think that actually works

14. dtan5457

where would a Z come up though? or is that for x+2

15. anonymous

i used 2 with z it is too weird

16. dtan5457

so it would be impossible with z?

17. anonymous

i am wagering it is 2

18. anonymous

i wonder if we can do it with differentiation though, is that part of this class?

19. dtan5457

this is pre calc we only did difference quotients so far

20. anonymous

maybe @Zarkon has a better idea seems like it needs to use inverse functions some how but i am clogged up in any case i am almost certain the (third) answer i wrote above works, just trying to figure how to subtract 2 in the denominator

21. anonymous

take the reciprocal, subtract 2 in the numerator, then take the reciprocal again of course that mess i wrote can be cleaned up without using compound fractions

22. dtan5457

my teacher may have wrote something wrong of some sort its only been like 2 weeks into school i doubt he would have something harder than you can solve

23. anonymous

usually you are told $$f$$ and $$f\circ g$$ and asked to find $$g$$ that you can do by finding the inverse of $$f$$ and applying it this is a bit different

24. dtan5457

you are right in my class example we had to find g and that was fairly simple