## stevench 3 years ago if f(g(x))=x and f(x)= 3x-4, find g(x)

1. hba

to find the inverse function, let y=g(x) f(y)=x 3y-4= x rearrange to find y and voila ! you get g(x)

2. hba

Notice that \[f(g(x))=x=f(f^{-1}(x))\] thus \[g(x) = f^{-1}(x)\]

3. hba

@stevench got it ?

4. stevench

i got it, but dont know how to re arrange it to where it fits in the options im given

5. hba

What did you get ? and What are your options ?

6. stevench

a) x-4/3 b) x+4/3 c) (x/3) +4 d) (x/3) -4

7. hba

What answer did you get ? @stevench

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9. hba

What answer did you get ?

10. stevench

I'm trying to do a billion things at once becaus I'm way overdue in an online class and just need help gettin answers

11. hba

You dont know how to solve 3y-4=x

12. hba

Just rearrange to find y

13. hba

14. hba

15. ikhwanz

easily you arrange it \[(f^-1(f(g(x))\] put the value of f(g(x)) inside f^-1 f-1=(x+4)/3_________ which from f(x)=3x-4 so change y=3x-4 then get the x value y+4/3 change f(y) to f-1=(x+4)/3 subtitute value fg(x) inside f-1

16. hba

@stevench You should also look at the CoC.

17. stevench

Thank you @ikhwanz for helping me find the answer

18. amistre64

As a rule of thumb, we would prefer the askers to participate in the solution process instead of having the answerers doing all the work. if f(g(x))=x and f(x)= 3x-4, find g(x) f(x)= 3x-4; replace x with a g(x) to get f(g(x))= 3[g(x)] - 4 ; and since f(g(x))=x x = 3[g(x)] - 4 , use basic algebra techniques to find g(x)

19. stevench

well at the moment in everything that i am trying to do I can't just simply wait all day

20. amistre64

thats not really our concern; we are aimed at being a study site, not a free answering service. We would rather promote learning the material as opposed to just handing over answers. This social contract is aimed at curbing people from using the site to cheat with ...

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