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

1. ## 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?

2. 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?

3. 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

4. ## 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?

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

6. ## clever~~~

wow, you are soooo clever~~ ^^

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

7. 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?

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

9. ## Oh no

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) ?

10. Originally Posted by Avatariko
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.

11. 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