# inverse of x+sin(X)

• Dec 17th 2008, 05:18 AM
horak
inverse of x+sin(X)
i want to know how calculate the inverse of x+sin(x).
thanks
• Dec 17th 2008, 12:43 PM
ThePerfectHacker
Quote:

Originally Posted by horak
i want to know how calculate the inverse of x+sin(x).
thanks

We can show the inverse exists by working with the fact that $( x + \sin x) ' > 0$ for $x\not = \pi n$ and $0$ for $x=\pi n$. Therefore, the function is increasing. But to since the inverse you need to be able to solve the equation $y + \sin (y) = x$. I do not think there is a "nice" way to solve this equation.