What is x if the function arcsin(3-2x) exists?

We'll impose the constraint for the arcsin(3-2x) to
exist:

-1 =< 3-2x =<
1

We'l solve the left side
inequality:

-1 =< 3 -
2x

-1 - 3 =< -2x

-4
=< -2x => 4 >= 2x => 4/2 >=
x

x =< 2

We'll solve
the right side inequality:

3-2x =<
1

-2x =< 1 - 3

-2x
=< -2

x >= 2/2

x
>= 1

The values of x, for the function
arcsin(3-2x) to exist, belong to the closed interval [1 ;
2].