The function is
.
Find the inverse function.
\Change
to
.

Interchange
and
.
.
Divide each side by
.

Apply inverse trigonometric property:
.

Subtract each side by
.


The inverse function is
.
Find the range of
:

.
Range of the sine function:
.
Here, 

.
Thus, the range of
is
.
The Domain of of
is range of
.
Range of
is
.
Domain of
is
. \ \
The Range of of
is domain of
.
Range of of
is
or
.
The inverse function is
.
The range of
is
.
The domain of
is
.
The Range of
is
.