Determine the inverse of the function:
$\displaystyle
f(x)=x+sinx
$
The function is both one-one as well as onto since
$\displaystyle f'(x)=1+cosx\geq 0$ for all real x.i.e. $\displaystyle f(x)$ is an incresing function and will never repeat its value
From the graph it appears as if the inverse is $\displaystyle f^{-1}(x)=x-sinx$ since it appears to be reflection of $\displaystyle f(x)$ with respect to the line $\displaystyle y=x$ as mirror.I am not sure about this though.
I am looking for verification