2

I'm attempting to find $$f^{-1}(x)$$ for the function $$f(x) = x + \sin{x}.$$ So far I've tried some simple algebraic methods as well as rewriting $\sin{x}$ as a power series. I'm not quite sure where to go aside from that. Any direction would be appreciated!

JoDraX
  • 258
  • 5
    While the inverse does exist, there isn't really a way of expressing it using elementary functions. You might like to check out this related question: http://math.stackexchange.com/questions/257873/why-isnt-the-inverse-of-the-function-x-mapsto-x-sinx-expressible-in-terms?rq=1 – mi986 May 27 '15 at 05:09
  • Why do you need the inverse? What are you trying to us it for? Depending on that different forms of non-closed form inverses may be differently useful. – DRF May 27 '15 at 07:10
  • This question already has an answer here: https://math.stackexchange.com/questions/257873/why-isnt-the-inverse-of-the-function-x-mapsto-x-sinx-expressible-in-terms/2623859#2623859 – IV_ Jan 27 '18 at 19:31

0 Answers0