Answer:
a. (f+g)(-3) means we need to add the two functions f and g, and then evaluate the sum at x=-3. So, we have:
(f+g)(-3) = f(-3) + g(-3) = [(-3)² - 3(-3)] + [2 - (-3)³]
= [9 + 9] + [2 + 27]
= 46
Therefore, (f+g)(-3) = 46.
b. (g-f)(1) means we need to subtract the function f from g, and then evaluate the difference at x=1. So, we have:
(g-f)(1) = g(1) - f(1) = [2 - 1³] - [(1)² - 3(1)]
= [2 - 1] - [1 - 3]
= 3
Therefore, (g-f)(1) = 3.
c. (f•g)(-2) means we need to multiply the two functions f and g, and then evaluate the product at x=-2. So, we have:
(f•g)(-2) = f(-2) • g(-2) = [(-2)² - 3(-2)] • [2 - (-2)³]
= [4 + 6] • [2 + 8]
= 100
Therefore, (f•g)(-2) = 100.
d. (g/f)(1) means we need to divide the function g by f, and then evaluate the quotient at x=1. So, we have:
(g/f)(1) = g(1) / f(1) = [2 - 1³] / [(1)² - 3(1)]
= [2 - 1] / [-2]
= -1/2
Therefore, (g/f)(1) = -1/2.
Explanation:
use brain