Answer:
Answer C --> y = 1/3 sin(x)
Step-by-step explanation:
When you are finding the inverse of a function, you are trying to obtain the function that applied to the one given gives you as result EXACTLY "x".
You know that the function sin(x) is the inverse of Arcsin(x), because when you applied it as follows, you obtain x (by cancelling out Arcsin and "liberating" the argument inside it: "x") :
[tex]sin(Arcsin(x))=x[/tex]
But in this case applying sin (x) to Arcsin (3x) will not render just x, because the argument that ARcsin is carrying is not just "x" but "3x":
[tex]sin(Arcsin(3x))= 3x[/tex]
So we need to divide by 3 as well in order to obtain just "x" after applying our inverse. The function that does such is the third one listed (C), sinc it also has a multiplicative 1/3 that will cancel the factor 3 we want to get rid of.
