Stating the largest value of a constant. Difficulty with trigno in functions.

Greetings all. :)

I have a simple question but which I am unable to do. It involves both functions and trignometry. The question is in 2 parts. I'll post the data, then the question.

Data:

function: g(x) = 3-2sinx

condition: 0 degrees <or= x <or= A degrees.

A is a constant.

The question (p1):

I am required to state the largest value of A for which g has an inverse.

Normally, this wouldn't be a problem if it weren't for that sin value. I'm not sure we can apply the same inverse method of replacing x and y that we normally do, so I don't really know what to do here.

(p2):

Obtain an expression in terms of x, for g^-1(x).

I can only do this once the value of A has been obtained.

Any help would be appreciated. :)