Question

1. What is (f⋅g)(x)?

Answer 1

Answer:

(f⋅g)(x)$= x^7 + 9x^4 - 9x^3 -81$

$(f - g)(x) = x^3 - 6x^2 + 18x + 6x - 10$

Step-by-step explanation:

For the first part of the question we have two functions

$f(x) = x^4 -9$

$g(x) = x^3 + 9$

If the expression refers to the multiplication of f and g, then:

(f⋅g)(x)$= f (x)g(x)$

So we multiply the function f(x) with the function g(x)

(f⋅g)(x)$= (x^4 - 9)(x^3 + 9)$

(f⋅g)(x)$= x^7 + 9x^4 - 9x^3 -81$

For the second part we have the functions:

$f(x) = x^3 -2x^2 + 12x - 6\\\\g(x) = 4x^2 - 6x + 4$

We wish to find (f - g) (x). We know that

$(f - g)(x) = f(x) - g(x)\\\\(f - g)(x) = x^3 - 2x^2 + 12x - 6 - [4x^2 - 6x + 4]\\\\(f - g)(x) = x^3 - 2x^2 + 12x - 6 -4x^2 + 6x - 4$

$(f - g)(x) = x^3 - 6x^2 + 18x + 6x - 10$