If f (x) = 3x^2 and g (x) = 2x+2, find

a) f (g (x)

b) fg (2)

c) gf (x)

Step-by-step explanation:

hello:

f (x) = 3x² and g (x) = 2x+2

a) f (g (x)) = f (2x+2) = 3 (2x+2) ²

b) f (g (2)) = 3 (2 (2) + 2) ² = 108

c) g (f (x)) = g (3x²) = 2 (3x²) + 2=6x²+2

see explanation

Step-by-step explanation:

(a)

f (g (x)) = f (2x + 2) = 3 (2x + 2) ² = 3 (4x² + 8x + 4) = 12x² + 24x + 12

(b)

Substitute x = 2 into f (g (x)), that is

f (g (2)) = 12 (2) ² + 24 (2) + 12 = 12 (4) + 48 + 12 = 48 + 48 + 12 = 108

(c)

g (f (x)) = g (3x²) = 2 (3x²) + 2 = 6x² + 2