Question 1187530
(g-f)(a) is equal to g(a) - f(a).
g(a) = -3a^2+3a^3+2a-4
f(a) = a^3+5a^2-2a+4
you subtract like terms from like terms.
3a^3 - a^3 = 2a^3
-3a^2 - 5a^2 = -8a^2
2a - -2a = 4a
-4 - 4 = -8
your resultant equation is (g-f)(a) = 2a^3 - 8a^2 + 4a - 8


to see if you did it correctly, assign a random value to a.
i used 7.


(g-f)(a) = 2a^3 - 8a^2 + 4a - 8 = 314 when a = 7.


g(a) = -3a^2 + 3a^3 + 2a - 4 = 892 when a = 7.


f(a) = a^3 + 5a^2 - 2a + 4 = 578 when a = 7.


892 - 578 =  314.


you get the same answer when you let a = 7.
(g-f)(a) = 314
g(a) = 892
f(a) = 578
g(a) - f(a) = 314.


this confirms that (g-f)(a) = g(a) - f(a) was evaluated correctly.