For the Given Functions F and G, Find the Requested $f ( x ) = 5 x ^ { 3 } + 3 ; g ( x ) = 3 x ^ { 2 } + 2 ; \quad$

For the given functions f and g, find the requested function and state its domain. Write the domain in interval notation.
- $f ( x ) = 5 x ^ { 3 } + 3 ; g ( x ) = 3 x ^ { 2 } + 2 ; \quad$ Find $f \cdot g$ .

A) $( f \cdot g ) ( x ) = 15 x ^ { 5 } + 10 x ^ { 3 } + 9 x ^ { 2 } + 6 ; ( \infty , 0 ) \cup ( 0 , \infty )$
B) $( f \cdot g ) ( x ) = 5 x ^ { 3 } + 3 x ^ { 2 } + 6 ; ( \infty , \infty )$
C) $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 15 \mathrm { x } ^ { 5 } + 10 \mathrm { x } ^ { 3 } + 9 \mathrm { x } ^ { 2 } + 6 ; ( \infty , \infty )$
D) $( f \cdot g ) ( x ) = 15 x ^ { 6 } + 10 x ^ { 3 } + 9 x ^ { 2 } + 6 ; ( \infty , \infty )$