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Math Help - Inverse of f(x)=x^Sin(x)...

  1. #1
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    Unhappy Inverse of f(x)=x^Sin(x)...

    I just need one question.
    Find the inverse of f(x) = x^Sin(x)
    this is it. can anyone help meee?
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  2. #2
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    Quote Originally Posted by Avatariko View Post
    I just need one question.
    Find the inverse of f(x) = x^Sin(x)
    the inverse of f(x) = x^{\sin{x}} cannot be found using elementary algebraic methods.

    what problem led you to this question?
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  3. #3
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    You can express f(x)=x^{\sin(s)} as a power series and then calculate the inverse of the series although I'm not sure how to determine the radius of convergence. Here's a reference:

    Inverse Functions

    So being the Mathematica head that I am, I calculated the first 10 terms of this inverse series with center at x=3:

    Code:
    In[45]:= g[x_] = 
    Normal[InverseSeries[N[Series[x^Sin[x], {x, 3, 10}]]]]
    
    Out[45]= 3. - 0.822989 (-1.1677 + x) + 0.0820429 (-1.1677 + x)^2 - 
     0.262188 (-1.1677 + x)^3 + 0.0118825 (-1.1677 + x)^4 - 
     0.180992 (-1.1677 + x)^5 - 0.0290483 (-1.1677 + x)^6 - 
     0.16546 (-1.1677 + x)^7 - 0.0691759 (-1.1677 + x)^8 - 
     0.180742 (-1.1677 + x)^9 - 0.120446 (-1.1677 + x)^10
    and then tested it with f(3.4):

    Code:
    In[39]:= f[x_] := x^Sin[x];
    yval = N[f[3.4]]
    xval = g[yval]
    
    Out[40]= 0.731451
    
    Out[41]= 3.39998
    Not too bad.
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  5. #5
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    Thank you for the big help!

    thanks for people. but i have made a mistake in my question.
    it was not f(x) = x^Sin(x)
    it was f(x) = x*Sin(x) [x multiply by Sin(x)]
    Im sorry.

    now can anyone find the inverse of that?
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  6. #6
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    By this time I really recommend you practice more, so you can be able to identify which rules to use faster.
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  7. #7
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    clever~~~

    wow, you are soooo clever~~ ^^

    thank you so much, now i can get the EX points from my teacher
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  8. #8
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    Quote Originally Posted by Avatariko View Post
    wow, you are soooo clever~~ ^^

    thank you so much, now i can get the EX points from my teacher
    maybe I'm missing something ... are you looking for the inverse of the function, or the derivative of the function?
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  9. #9
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    . . . I want my money back if he wanted just the derivative.
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  10. #10
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    Oh no

    this was not the answer...
    because i want to find the INVERSE of this function.
    Not DERIVATIVE...

    does anyone have any ideas for the INVERSE of f(x) = x・Sin(x) ?
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  11. #11
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    Quote Originally Posted by Avatariko View Post
    this was not the answer...
    because i want to find the INVERSE of this function.
    Not DERIVATIVE...

    does anyone have any ideas for the INVERSE of f(x) = x・Sin(x) ?
    one more time ...

    you cannot find the inverse of that function using elementary methods ... see
    shawsend's original post.
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  12. #12
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    Quote Originally Posted by Avatariko View Post
    thanks for people. but i have made a mistake in my question.
    it was not f(x) = x^Sin(x)
    it was f(x) = x*Sin(x) [x multiply by Sin(x)]
    Im sorry.

    now can anyone find the inverse of that?
    Popular question: http://www.mathhelpforum.com/math-he...x-inverse.html

    Thread closed.
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