Answer:
(f⋅g)(x)[tex] = x^7 + 9x^4 - 9x^3 -81[/tex]
[tex](f - g)(x) = x^3 - 6x^2 + 18x + 6x - 10[/tex]
Step-by-step explanation:
For the first part of the question we have two functions
[tex]f(x) = x^4 -9[/tex]
[tex]g(x) = x^3 + 9[/tex]
If the expression refers to the multiplication of f and g, then:
(f⋅g)(x)[tex] = f (x)g(x)[/tex]
So we multiply the function f(x) with the function g(x)
(f⋅g)(x)[tex] = (x^4 - 9)(x^3 + 9)[/tex]
(f⋅g)(x)[tex] = x^7 + 9x^4 - 9x^3 -81[/tex]
For the second part we have the functions:
[tex]f(x) = x^3 -2x^2 + 12x - 6\\\\g(x) = 4x^2 - 6x + 4[/tex]
We wish to find (f - g) (x). We know that
[tex](f - g)(x) = f(x) - g(x)\\\\(f - g)(x) = x^3 - 2x^2 + 12x - 6 - [4x^2 - 6x + 4]\\\\(f - g)(x) = x^3 - 2x^2 + 12x - 6 -4x^2 + 6x - 4[/tex]
[tex](f - g)(x) = x^3 - 6x^2 + 18x + 6x - 10[/tex]
