I just need one question.

Find the inverse of f(x) = x^Sin(x)

this is it. can anyone help meee?(Crying)

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- Sep 24th 2009, 02:03 PMAvatarikoInverse 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 PMskeeter
- Sep 24th 2009, 04:06 PMshawsend
You can express $\displaystyle f(x)=x^{\sin(s)}$ 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

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 PMArturo_026
- Sep 24th 2009, 04:17 PMAvatarikoThank 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 PMArturo_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 PMAvatarikoclever~~~
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 PMskeeter
- Sep 24th 2009, 05:03 PMshawsend
. . . I want my money back if he wanted just the derivative.

- Sep 25th 2009, 03:09 PMAvatarikoOh no
this was not the answer...

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 PMskeeter
- Sep 25th 2009, 03:58 PMmr fantastic
Popular question: http://www.mathhelpforum.com/math-he...x-inverse.html

Thread closed.