anonymous
  • anonymous
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
f(x)=9x+3 g(x)=x-3/9
anonymous
  • anonymous
please help!!
atlas
  • atlas
when you calculate f(g(x)) : think this way: g(x) is the new substitution of x. So replace x with the value you have for g(x) in f(x) You will get f(g(x)) this way

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atlas
  • atlas
Similarly calculate g(f(x))
anonymous
  • anonymous
so f(g(x)) will equal 9(x-3)+3? What do i have to do after that?
DebbieG
  • DebbieG
Remember what function notation means: it means that you "plug in" whatever is in the ( ) for the variable in the definition of the function, right? \(\Large g(x)=(x-3)/9\\ \text{then } \Large g(6)=(6-3)/9\\ \text{and } \Large g(a)=(a-3)/9\\ \text{and } \Large g(r+1)=[(r+1)-3]/9\) So to find g(f(x)) you'll just want to plop f(x) into g(x) in place of the variable x, and simplify the resulting expression: \(\Large g(f(x))=g(9x+3)=[(9x+3)-3]/9\) Simplify that, and you'll see that you get x. Now do the same thing, inthe other direction, that is, find f(g(x)). You should also get x (but show each step!)
DebbieG
  • DebbieG
What you said above is not correct for f(g(x)).
DebbieG
  • DebbieG
\(\Large g(x)=(x-3)/9\\ \text{and } \Large f(x)=9x+3\\\) then \[\Large f(g(x))=f(\frac{ x-3 }{ 9 } ) = 9(\frac{ x-3 }{ 9 } )+3\]
DebbieG
  • DebbieG
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anonymous
  • anonymous
how would you simplify it after your plugged it in? I just need to understand how it would be done for f(x). So once you get that f(g(x)=9(x-3/9) + 3 what do i have to do after that, if you dont mind.
DebbieG
  • DebbieG
Just use some basic algebra :) \(\Large \cancel9(\dfrac{ x-3 }{ \cancel 9 } )+3\) Now what do you get?
anonymous
  • anonymous
ahhh! you will then be left with x-3+3 and the 3s will be negated leaving the answer to be x right??
DebbieG
  • DebbieG
Remember, if you know for certain that f and g are inverses (e.g., the problem tells you THAT THEY ARE, not asks you to DETERMINE WHETHER THEY ARE) then when you take the two compositions: f(g(x)) and g(f(x)) everything should just fallll right into place so that each simplifies to x. That's what it means for them to be inverses. :)
DebbieG
  • DebbieG
Exactly right! :)
anonymous
  • anonymous
Wow! Thank you so so much!! This really clears up everything! :) Thank you again for your help! :)
DebbieG
  • DebbieG
you're very welcome. :) happy to help. And welcome to Open Study!! :)

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