anonymous
  • anonymous
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. f(x) = x-7/x+3 and g(x)=-3x-7/x-1
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
\[f(x)=\frac{x-7}{x+3}\] replace \(x\) by \(\frac{-3-7}{x-1}\) and get \[f(g(x))=\frac{\frac{-3-7}{x-1}-7}{\frac{-3-7}{x-1}+3}\]
anonymous
  • anonymous
bunch of algebra follows multiply top and bottom by \(x-1\) to clear the fraction then a raft of cancellation will ensue, ending only with \(x\)
anonymous
  • anonymous
can you show me its very confusing

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Hero
  • Hero
That's the hard way to do it. And geez, @satellite you're a genius at typing so fast.
anonymous
  • anonymous
copy and past is all i did
anonymous
  • anonymous
and if you have an easier way i am all eyes
anonymous
  • anonymous
*paste
Hero
  • Hero
You simply reduce one of the expressions to a mixed number. That way it only has one x value. If you wanted to, you could reduce both of them that way. For example: \[\frac{x - 7}{x + 3} = \frac{x + 3 - 10}{x + 3} = \frac{x + 3}{x + 3} - \frac{10}{x + 3} = 1 - \frac{10}{x + 3}\]
Hero
  • Hero
Now you have one x to insert g(x) into f(x)
Hero
  • Hero
\[f(g(x)) = 1 - \frac{10}{\frac{-3x - 7}{x -1} + 3}\]
anonymous
  • anonymous
i can't wait to see this ...
Hero
  • Hero
It's easier to do on paper than type it out. I've already done this before. I helped another student with the exact same kind of problem.
Hero
  • Hero
But I at least was able to help reduce it so that you're inserting g(x) only once.
anonymous
  • anonymous
ok :)
anonymous
  • anonymous
there is no such thing as a free lunch
anonymous
  • anonymous
ill try to solve it
anonymous
  • anonymous
\[=\frac{\frac{-3x-7}{x-1}-7}{\frac{-3x-7}{x-1}+3}\times \frac{x-1}{x-1}\] \[=\frac{-3x-7-7(x-1)}{-3x-7+3(x-1)}\]
anonymous
  • anonymous
distribute?
anonymous
  • anonymous
is there a typo here?
anonymous
  • anonymous
oh no it is right yeah distribute combine like terms, etc you will get it but i do like @hero method
Hero
  • Hero
Basically, I re-wrote it like this: \[1 - 10 \div \left(\frac{-3x - 7}{x - 1} + 3\right)\]\[1 - 10 \div \left(\frac{-3x - 7 + 3(x -1)}{x-1}\right)\]\[1 - 10 \times \left(\frac{x - 1}{-10}\right)\]\[1 + x - 1\]
anonymous
  • anonymous
but you are supposed to get \(x\)
Hero
  • Hero
\[1 - 1 + x = x\]
anonymous
  • anonymous
how do you get the 10
anonymous
  • anonymous
i am just funnin
anonymous
  • anonymous
the 10 was a trick
Hero
  • Hero
@melchar, look at my second post.
anonymous
  • anonymous
thank you!

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