anonymous
  • anonymous
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. f(x) = the quantity x minus seven divided by the quantity x plus three. and g(x) = quantity negative three x minus seven divided by quantity x minus one.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[f(x)=\frac{ x-7 }{ x+3 } g(x)=\frac{ -3x-7 }{ x-1 }\]
anonymous
  • anonymous
prepare to do a raft of algebra
anonymous
  • anonymous
ah okay thank you for your help in advance btw :)

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anonymous
  • anonymous
\[f(x)=\frac{ x-7 }{ x+3 } \] and \[g(x)=\frac{ -3x-7 }{ x-1 }\] right?
anonymous
  • anonymous
yes
anonymous
  • anonymous
this is amazingly easy for me to write the composition one way by using copy and paste i am going to past \(g(x)=\frac{ -3x-7 }{ x-1 }\)where every i see an \(x\) in \(f(x)=\frac{ x-7 }{ x+3 }\)
anonymous
  • anonymous
\[f(x)=\frac{ x-7 }{ x+3 }\] \[f(g(x))=\frac{ \frac{ -3x-7 }{ x-1 }-7 }{ \frac{ -3x-7 }{ x-1 }+3 }\]
anonymous
  • anonymous
okay i did that and now do i just solve?
anonymous
  • anonymous
now comes the raft of algebra part
anonymous
  • anonymous
which will end up with an orgy of cancellation since your answer should be \(x\)
anonymous
  • anonymous
it is not really that bad multiply top and bottom of that complex fraction by \(x-1\) to clear the denominator don't forget the distributive law
anonymous
  • anonymous
okay let me just do it real quick
anonymous
  • anonymous
would i do the same for the g(f(x)) = x. later on?
anonymous
  • anonymous
yes, just clear the denominators then all will go bye bye
anonymous
  • anonymous
ah thank you so much!
anonymous
  • anonymous
yw
anonymous
  • anonymous
wait im so lost what happens with the -7 and 3?
anonymous
  • anonymous
don't forget the distributive law !!
anonymous
  • anonymous
????
anonymous
  • anonymous
\[\frac{ \frac{ -3x-7 }{ x-1 }-7 }{ \frac{ -3x-7 }{ x-1 }+3 }\times \frac{x-1}{x-1}\] \[=\frac{-3x-7(x-1)}{-3x-7+3(x-1)}\] is a start
anonymous
  • anonymous
the distributive law in action denominators go, but you still have to distribute now distribute again, the -7 up top and the 3 below then combine like terms
anonymous
  • anonymous
okay at the denominator should i add the 7 and 3 before distrubuting or no?
anonymous
  • anonymous
distribute first
anonymous
  • anonymous
numerator should be \(-10x+7\) if you do it correctly
anonymous
  • anonymous
okay just a min
anonymous
  • anonymous
the denom i got -10
anonymous
  • anonymous
yeah that is right, and i lied, the numerator is \(-3x-7-7(x-1)=-3x-7-7x+7=-10x\)
anonymous
  • anonymous
and of course \(\frac{-10x}{-10}=x\) as needed
anonymous
  • anonymous
ah okay thats easy in reality thanks! ill do the other side now
anonymous
  • anonymous
good luck it is real similar
anonymous
  • anonymous
i just am stuck a little after muliplying x+3/x+3
anonymous
  • anonymous
\[g(x)=\frac{ -3x-7 }{ x-1 }\] \[g(f(x))=\frac{ -3\frac{ x-7 }{ x+3 }-7 }{ \frac{ x-7 }{ x+3 }-1 }\]
anonymous
  • anonymous
yeah i did that already
anonymous
  • anonymous
multiply by \(x-3\) what did you get in the numerator ?
anonymous
  • anonymous
why x-3?
anonymous
  • anonymous
typo i meant \(x+3\)
anonymous
  • anonymous
okay making sure ahha
anonymous
  • anonymous
-3(x-7)-7 is my numerator?
anonymous
  • anonymous
before distributing etc you should be looking at \[-3(x-7)-7(x+3)\]
anonymous
  • anonymous
forgot that distributive law didn't you?
anonymous
  • anonymous
ah yes
anonymous
  • anonymous
it is the distributive LAW, not the distributive option
anonymous
  • anonymous
hahaha yes so my numerator is:(-3x+21)-7x-21
anonymous
  • anonymous
numerator comes to -10x
anonymous
  • anonymous
got it perfect! thanks!
anonymous
  • anonymous
yw

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