Answer:
(g*f)(x) = 3x^5
(g - f)(x) = x^2(3 - x)
(g + f)(2) = 20
Explanation:
The given functions are
f(x) = x^3
g(x) = 3x^2
1) To find (g*f)(x), we would multiply both functions. Thus,
(g*f)(x) = x^3 * 3x^2
(g*f)(x) = 3x^(3 + 2)
(g*f)(x) = 3x^5
2) To find (g-f)(x), we would subtract f(x) from g(x). Thus,
(g - f)(x) = 3x^2 - x^3
By factorizing,
(g - f)(x) = x^2(3 - x)
3) To find (g + f)(2), the first step is to find (g + f)(x). We would add both functions. It becomes
(g + f)(x) = 3x^2 + x^3
We would find (g + f)(2) by substituting x = 2 into (g + f)(x). Thus,
(g + f)(2) = 3(2)^2 + 2^3 = 12 + 8
(g + f)(2) = 20
