For the given functions f and g, find the requested function and state its domain.
-$f ( x ) = 5 x ^ { 3 } - 2 ; g ( x ) = 5 x ^ { 2 } + 3$
Find $f \cdot g$.
A) $( f \cdot g ) ( x ) = 5 x ^ { 3 } + 5 x ^ { 2 } - 6$; all real numbers
B) $( f \cdot g ) ( x ) = 25 x ^ { 6 } + 15 x ^ { 3 } - 10 x ^ { 2 } - 6$; all real numbers
C) $( f \cdot g ) ( x ) = 25 x ^ { 5 } + 15 x ^ { 3 } - 10 x ^ { 2 } - 6$; all real numbers
D) $( f \cdot g ) ( x ) = 25 x ^ { 5 } + 15 x ^ { 3 } - 10 x ^ { 2 } - 6 ; \{ x \mid x \neq 0 \}$

Question

For the given functions f and g, find the requested function and state its domain.
-$f ( x ) = 5 x ^ { 3 } - 2 ; g ( x ) = 5 x ^ { 2 } + 3$
Find $f \cdot g$. 
A) $( f \cdot g ) ( x ) = 5 x ^ { 3 } + 5 x ^ { 2 } - 6$; all real numbers
B) $( f \cdot g ) ( x ) = 25 x ^ { 6 } + 15 x ^ { 3 } - 10 x ^ { 2 } - 6$; all real numbers
C) $( f \cdot g ) ( x ) = 25 x ^ { 5 } + 15 x ^ { 3 } - 10 x ^ { 2 } - 6$; all real numbers
D) $( f \cdot g ) ( x ) = 25 x ^ { 5 } + 15 x ^ { 3 } - 10 x ^ { 2 } - 6 ; \{ x \mid x \neq 0 \}$

Quizplus · Accepted Answer

The product $f \cdot g$ is found by multiplying the functions: $(5x^3 - 2)(5x^2 + 3) = 25x^5 + 15x^3 - 10x^2 - 6$. The domain is all real numbers since there are no restrictions from division or square roots.

For the Given Functions F and G, Find the Requested f(x)=5x3−2;g(x)=5x2+3f ( x ) = 5 x ^ { 3 } - 2 ; g ( x ) = 5 x ^ { 2 } + 3f(x)=5x3−2;g(x)=5x2+3

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