For the Given Functions F and G, Find the Requested $$f ( x ) = 2 x ^ { 3 } - 1 ; g ( x ) = 5 x ^ { 2 } + 2$$

Multiple Choice

For the given functions f and g, find the requested function and state its domain.
- $$f ( x ) = 2 x ^ { 3 } - 1 ; g ( x ) = 5 x ^ { 2 } + 2$$
Find $f \cdot g$ .

A) $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 10 \mathrm { x } ^ { 5 } + 4 \mathrm { x } ^ { 3 } - 5 \mathrm { x } ^ { 2 } - 2$ ; all real numbers
B) $( f \cdot g ) ( x ) = 10 x ^ { 6 } + 4 x ^ { 3 } - 5 x ^ { 2 } - 2$ ; all real numbers
C) $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = 2 \mathrm { x } ^ { 3 } + 5 \mathrm { x } ^ { 2 } - 2 ;$ all real numbers
D) $( f \cdot g ) ( x ) = 10 x ^ { 5 } + 4 x ^ { 3 } - 5 x ^ { 2 } - 2 ; \{ x \mid x \neq 0 \}$