Inverse of f(x)=x^Sin(x)...

• Sep 24th 2009, 02:03 PM
Avatariko
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?(Crying)
• Sep 24th 2009, 03:01 PM
skeeter
Quote:

Originally Posted by Avatariko
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?
• Sep 24th 2009, 04:06 PM
shawsend
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
• Sep 24th 2009, 04:14 PM
Arturo_026
• Sep 24th 2009, 04:17 PM
Avatariko
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?(Doh)
• Sep 24th 2009, 04:20 PM
Arturo_026
By this time I really recommend you practice more, so you can be able to identify which rules to use faster.http://www4a.wolframalpha.com/Calcul...image/gif&s=18
• Sep 24th 2009, 04:31 PM
Avatariko
clever~~~
wow, you are soooo clever~~ ^^

thank you so much, now i can get the EX points from my teacher(Giggle)
• Sep 24th 2009, 05:01 PM
skeeter
Quote:

Originally Posted by Avatariko
wow, you are soooo clever~~ ^^

thank you so much, now i can get the EX points from my teacher(Giggle)

maybe I'm missing something ... are you looking for the inverse of the function, or the derivative of the function?
• Sep 24th 2009, 05:03 PM
shawsend
. . . I want my money back if he wanted just the derivative.
• Sep 25th 2009, 03:09 PM
Avatariko
Oh no
because i want to find the INVERSE of this function.
Not DERIVATIVE...(Wondering)

does anyone have any ideas for the INVERSE of f(x) = x・Sin(x) ?
• Sep 25th 2009, 03:15 PM
skeeter
Quote:

Originally Posted by Avatariko
because i want to find the INVERSE of this function.
Not DERIVATIVE...(Wondering)

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.
• Sep 25th 2009, 03:58 PM
mr fantastic
Quote:

Originally Posted by Avatariko
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?(Doh)

Popular question: http://www.mathhelpforum.com/math-he...x-inverse.html