If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (g – f)(3)?

a) 6 – 3 – (4 + 3)2

b) 6 – 3 – (4 – 32)

c) 6(3) – 4 + 32

d) 6(3) – 4 – 32

I hope this helps you

F(x) = 4 - x^2
g(x) = 6x
(g - f)(x) = 6x - (4 - x^2)
(g - f)(3) = 6(3) - (4 - 3^2) = 6(3) - 4 + 3^2

First of all, you can distribute ( g - f ) 3 which gives you g (3) - f (3) . Now we know what to find. You plug in 3 to g (x) and f (x) .

f (3) = 4 - 2 (3)f (3) = 4 - 6f (3) = -2
g (3) = 6 (3)g (3) = 18
Now since we know what f (3) and g (3) is, we can plug it in to ( g - f ) 3 which I simplifed at the beginning to g (3) -  f (3) .

g (3) - f (3)= (18) - ( -2)= 18 + 2
= 20
Now since we know what it equals, we have to simplify all the answer choices to see which one is equal.
A:6 - 3 - ( 4 + 3) 2 = 6 - 3 - ( 8 + 6)= 6 - 3 - 14= 3 - 14= -11
B:6 - 3 - ( 4 - 32 )
=6 - 3 - ( -28 )
= 6 - 3 + 28= 3 + 28= 31
C:( 6 ) ( 3 ) - 4 + 32
= 18 - 4 + 32= 14 + 32= 46
D:6 ( 3 ) - 4 - 32= 18 - 4 - 32= 14 - 32= -18
Wow, would you look at that. None of the expressions are equal to 20. There is probably an error in the question. See if you made a typo or if it is written/typed like this, ask your teacher or whoever you got it from. I hope this helped you. :D