Question

select the correct answer from each drop-down menu.
if $f(x) = 0.5x^2 - 2$ and $g(x) = 8x^3 + 2$, find the value of the following function.
$(f \cdot g)(x) = \boxed{4} x^5 - \boxed{16} x^3 + \boxed{\phantom{0}} x^2 - \boxed{4}$
options: 2.5, 0, 1, 5

Explanation:

Step1: Define product of functions

$(f \cdot g)(x) = f(x) \cdot g(x)$

Step2: Substitute given functions

$(f \cdot g)(x) = (0.5x^2 - 2)(8x^3 + 2)$

Step3: Expand using distributive property

$(f \cdot g)(x) = 0.5x^2 \cdot 8x^3 + 0.5x^2 \cdot 2 - 2 \cdot 8x^3 - 2 \cdot 2$

Step4: Compute each term

$(f \cdot g)(x) = 4x^5 + x^2 - 16x^3 - 4$

Step5: Rearrange terms by degree

$(f \cdot g)(x) = 4x^5 - 16x^3 + 1x^2 - 4$

Answer:

The missing coefficient is $\boldsymbol{1}$