Find the Domain of the Function F and of Its $\mathrm { f } ^ { - 1 }$

Find the domain of the function f and of its inverse function $\mathrm { f } ^ { - 1 }$ .
- $$f ( x ) = 2 \sin ( 3 x - 1 )$$

A) Domain of $f : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ - 3,3 ]$

B) Domain of f: $\left[ - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right]$
Domain of $\mathrm { f } ^ { - 1 } : ( \infty , \infty )$

C) Domain of $f : [ - 2,2 ]$
Domain of $\mathrm { f } ^ { - 1 } : ( \infty , \infty )$

D) Domain of $\mathrm { f } : ( \infty , \infty )$

Domain of $f ^ { - 1 } : [ - 2,2 ]$