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

Multiple Choice

Find the domain of the function f and of its inverse function $\mathrm { f } ^ { - 1 }$ .
- $$f ( x ) = 3 \sin ( 5 x )$$

A) Domain of $f : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ 2,8 ]$

B) Domain of $\mathrm { f } : ( \infty , \infty )$
Domain of $\mathrm { f } ^ { - 1 } : [ - 5,5 ]$

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

D) Domain of $\mathrm { f } : \left[ - \frac { 1 } { 5 } , \frac { 1 } { 5 } \right]$

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