Given functions are:
[tex]f(x) = 0.5x^2-2[/tex]
and [tex]g(x) = 8x^3+2[/tex]
Using both functions we need to find value of (f*g)(x)
(f*g)(x) simply means find product of f(x) and g(x) so we will multiply values of each function as shown below:
[tex](f*g)(x) = (0.5x^2-2)(8x^3+2)[/tex]
[tex](f*g)(x) = 0.5x^2(8x^3+2)-2(8x^3+2)[/tex]
[tex](f*g)(x) = 4x^5+1x^2-16x^3-4[/tex]
[tex](f*g)(x) = 4x^5-16x^3+1x^2-4[/tex]
[tex](f*g)(x) = 4x^5-16x^3+x^2-4[/tex]
Hence final answer is [tex](f*g)(x) = 4x^5-16x^3+x^2-4[/tex].
