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Check Inverse Please

  1. Dec 15, 2004 #1
    f(x)=-1/7x-14 is the inverse of this f^-1(x)=[7(x+14)]/(-1) ? Can someone please check for me if not what did I do wrong? :redface:
     
  2. jcsd
  3. Dec 15, 2004 #2

    kreil

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    Gold Member

    To check an inverse:

    [tex]f(f^{-1}(x))=f^{-1}(f(x))=x[/tex]
     
  4. Dec 17, 2004 #3
    Its very easy ..
    put y = -1/(7x-14)
    and solve for x
    u will get
    x= (14y-1)/7y
    so the inverse function of f(x) is f-1(x) = (14x-1)/7x
     
  5. Dec 17, 2004 #4
    The question is (-1/7)x-14 is my answer incorrect? f^-1(x)=[7(x+14)]/-1?
    I dont know if the -1 is right and not sure about the answer either. :uhh:
     
  6. Dec 17, 2004 #5
    The -1 is correct and your answer is correct... I don't know how you got around to dividing by -1 as you must have used a different method, but it's correct nonetheless.

    If you want to check these problems by yourself in the future, an easy way is to graph both functions. They should reflect over the function f(x) = x
     
    Last edited: Dec 17, 2004
  7. Dec 17, 2004 #6
    This is what I did. x=(-1/7)y-14
    x+14=(-1/7)y
    7(x+14)=-1y
    divide both sides by -1 and get
    [7(x+14)]/-1 but can this be simplified? Can I get rid of the -1 somehow or is the correct way of writing it?
     
  8. Dec 17, 2004 #7
    Yes, dividing by -1 is basically the same as multiplying by -1 (in this situation). Make everything negative.

    [7(x+14)]/-1 yields:

    -7(x+14)

    which, simplified is:

    -7x-98
     
  9. Dec 17, 2004 #8
    how come x+14 is not multiplied by -1? and then by -7?
     
  10. Dec 17, 2004 #9
    Well, it's easier if you simplify first.

    [7(x+14)]/-1 can be simplified by multiplying 7(x+14).

    7(x+14) = (7x + 98) and now you can divide by -1

    (7x + 98)/-1 is the same thing as (7x/-1) + (98/-1) which brings the final result to:

    -7x - 98
     
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