For this case we have the following functions:
[tex]f (x) = 4-x ^ 2\\g (x) = 6x[/tex]
By definition we have to:
[tex](f-g) (x) = f (x) -g (x)\\(g-f) (x) = g (x) -f (x)[/tex]
Then, we find [tex](f-g) (x):[/tex]
[tex]f (x) -g (x) = 4-x ^ 2-6x = -x ^ 2-6x 4[/tex]
We evaluate the function in 3:
[tex](f-g) (3) = - (3) ^ 2-6 (3) 4 = -9-18 4 = -27 4 = -23[/tex]
Now we find[tex](g-f) (x):[/tex]
[tex]g (x) -f (x) = 6x- (4-x ^ 2) = 6x-4 x ^ 2 = x ^ 2 6x-4[/tex]
We evaluate the function in 3
[tex](g-f) (3) = 3 ^ 2 6 (3) -4 = 9 18-4 = 23[/tex]
Answer:
[tex](f-g) (3) = - 23\\(g-f) (3) = 23[/tex]
