Thread: 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?

Originally Posted by Avatariko

I just need one question.
Find the inverse of f(x) = x^Sin(x)

the inverse of cannot be found using elementary algebraic methods.

what problem led you to this question?

You can express 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.

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?

By this time I really recommend you practice more, so you can be able to identify which rules to use faster.

wow, you are soooo clever~~ ^^

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

Originally Posted by Avatariko

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?

. . . I want my money back if he wanted just the derivative.

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) ?

Originally Posted by Avatariko

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.

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?

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

Thread closed.