For the given functions f(x) and g(x), find f(x) ∙ g(x).
-$$f ( x ) = 5 x ^ { 6 } , g ( x ) = - 4 x ^ { 4 } + 8 x ^ { 2 } - 1$$
A) $- 20 x ^ { 4 } + 40 x ^ { 2 } - 5$
B) $- 20 x ^ { 10 } + 8 x ^ { 2 } - 1$
C) $- 20 x ^ { 10 } + 40 x ^ { 8 }$
D) $- 20 x ^ { 10 } + 40 x ^ { 8 } - 5 x ^ { 6 }$

Question

Quizplus · Accepted Answer

To find the product of two functions, we simply multiply each term of one function by each term of the other function.

\begin{align*}
f(x) \cdot g(x) &= (5x^6) \cdot (-4x^4 + 8x^2 - 1) \ 
&= -20x^{10} + 40x^8 - 5x^6
\end{align*}

Therefore, the best choice is D.

For the Given Functions F(x) and G(x), Find F(x) ∙ f(x)=5x6,g(x)=−4x4+8x2−1f ( x ) = 5 x ^ { 6 } , g ( x ) = - 4 x ^ { 4 } + 8 x ^ { 2 } - 1f(x)=5x6,g(x)=−4x4+8x2−1

For the Given Functions F(x) and G(x), Find F(x) ∙ $f ( x ) = 5 x ^ { 6 } , g ( x ) = - 4 x ^ { 4 } + 8 x ^ { 2 } - 1$