Given f (x) = 2x²+4x-6 and g (x) = 2x-2, find each function

1. (f/g) (x)

2. f (a + 2)

3. g (a/2)

F (x) = 2x²+4x-6 and g (x) = 2x-2, find each function

1. (f/g) (x) = f (x) : g (x) = (2x²+4x-6) : (2x-2)

First factor both top and bottom:

(2x-2) (x+3) : (2x-2) = x+3

2. f (a + 2) = plug (a+2) in anywhere there is an x in f (x) = 2x²+4x-6 - - >

2 (a+2) ^2 + 4 (a+2) - 6 = 2 (a^2+4a+4) + 4a+8-6, now distribute:

2a^2+8a+8+4a+2, combine like terms

2a^2+12a+10

3. g (a/2) = plug (a/2) in anywhere there's an x in g (x) = 2x-2:

2 (a/2) - 2 = a-2