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anonymous

  • one year ago

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.

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  1. anonymous
    • one year ago
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    \[f(x)=\frac{ x-7 }{ x+3 } g(x)=\frac{ -3x-7 }{ x-1 }\]

  2. anonymous
    • one year ago
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    prepare to do a raft of algebra

  3. anonymous
    • one year ago
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    ah okay thank you for your help in advance btw :)

  4. anonymous
    • one year ago
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    \[f(x)=\frac{ x-7 }{ x+3 } \] and \[g(x)=\frac{ -3x-7 }{ x-1 }\] right?

  5. anonymous
    • one year ago
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    yes

  6. anonymous
    • one year ago
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    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 \(f(x)=\frac{ x-7 }{ x+3 }\)

  7. anonymous
    • one year ago
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    \[f(x)=\frac{ x-7 }{ x+3 }\] \[f(g(x))=\frac{ \frac{ -3x-7 }{ x-1 }-7 }{ \frac{ -3x-7 }{ x-1 }+3 }\]

  8. anonymous
    • one year ago
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    okay i did that and now do i just solve?

  9. anonymous
    • one year ago
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    now comes the raft of algebra part

  10. anonymous
    • one year ago
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    which will end up with an orgy of cancellation since your answer should be \(x\)

  11. anonymous
    • one year ago
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    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

  12. anonymous
    • one year ago
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    okay let me just do it real quick

  13. anonymous
    • one year ago
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    would i do the same for the g(f(x)) = x. later on?

  14. anonymous
    • one year ago
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    yes, just clear the denominators then all will go bye bye

  15. anonymous
    • one year ago
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    ah thank you so much!

  16. anonymous
    • one year ago
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    yw

  17. anonymous
    • one year ago
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    wait im so lost what happens with the -7 and 3?

  18. anonymous
    • one year ago
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    don't forget the distributive law !!

  19. anonymous
    • one year ago
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    ????

  20. anonymous
    • one year ago
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    \[\frac{ \frac{ -3x-7 }{ x-1 }-7 }{ \frac{ -3x-7 }{ x-1 }+3 }\times \frac{x-1}{x-1}\] \[=\frac{-3x-7(x-1)}{-3x-7+3(x-1)}\] is a start

  21. anonymous
    • one year ago
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    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

  22. anonymous
    • one year ago
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    okay at the denominator should i add the 7 and 3 before distrubuting or no?

  23. anonymous
    • one year ago
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    distribute first

  24. anonymous
    • one year ago
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    numerator should be \(-10x+7\) if you do it correctly

  25. anonymous
    • one year ago
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    okay just a min

  26. anonymous
    • one year ago
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    the denom i got -10

  27. anonymous
    • one year ago
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    yeah that is right, and i lied, the numerator is \(-3x-7-7(x-1)=-3x-7-7x+7=-10x\)

  28. anonymous
    • one year ago
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    and of course \(\frac{-10x}{-10}=x\) as needed

  29. anonymous
    • one year ago
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    ah okay thats easy in reality thanks! ill do the other side now

  30. anonymous
    • one year ago
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    good luck it is real similar

  31. anonymous
    • one year ago
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    i just am stuck a little after muliplying x+3/x+3

  32. anonymous
    • one year ago
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    \[g(x)=\frac{ -3x-7 }{ x-1 }\] \[g(f(x))=\frac{ -3\frac{ x-7 }{ x+3 }-7 }{ \frac{ x-7 }{ x+3 }-1 }\]

  33. anonymous
    • one year ago
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    yeah i did that already

  34. anonymous
    • one year ago
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    multiply by \(x-3\) what did you get in the numerator ?

  35. anonymous
    • one year ago
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    why x-3?

  36. anonymous
    • one year ago
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    typo i meant \(x+3\)

  37. anonymous
    • one year ago
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    okay making sure ahha

  38. anonymous
    • one year ago
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    -3(x-7)-7 is my numerator?

  39. anonymous
    • one year ago
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    before distributing etc you should be looking at \[-3(x-7)-7(x+3)\]

  40. anonymous
    • one year ago
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    forgot that distributive law didn't you?

  41. anonymous
    • one year ago
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    ah yes

  42. anonymous
    • one year ago
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    it is the distributive LAW, not the distributive option

  43. anonymous
    • one year ago
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    hahaha yes so my numerator is:(-3x+21)-7x-21

  44. anonymous
    • one year ago
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    numerator comes to -10x

  45. anonymous
    • one year ago
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    got it perfect! thanks!

  46. anonymous
    • one year ago
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    yw

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