Given the functions f (x) = 3x and g (x) = x² + 1, find [ (gºf) (x) ] - [ (fºg) (x) ].

6x^2 - 2

Step-by-step explanation:

plug in f (x) into the g (x) formula given

g (f (x)) = (3x) ^2 + 1

simplify

= 9x^2+2

plug in g (x) into the f (x) formula given

f (g (x)) = 3 (x^2+1)

distribute

= 3x^2 + 3

set g (f (x)) - f (g (x))

(9x^2+2) - (3x^2+3)

carry the negative

9x^2+2-3x^2-3

simplify by combining like terms

6x^2-2