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If f(x)=x²-3x and g(x) = 2 - x³, evaluate the following.

a. (f+g)(-3)
b. (g-f) (1)
c. (f•g) (-2)
d. (g/f) (1)

User Albie
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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:

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User Fabio Picheli
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