Just use the definition of arcsin that is given by:
\(\left \{ {{sen \alpha =x} \atop {arcsinx= \alpha }} \right. \\ \\ arcsin(sen \alpha )= \alpha\)
Therefore:
\(f(x,y)=arcsin(sen(x+y)) \\ \boxed {f(x,y)=x+y}\)
If you notice any mistake in my english, please let me know, because i am not native.