Given: F (x) = 2x - 1; G (x) = 3x + 2; H (x) = x 2 Find F[G (x) ] - F (x). 4x + 4 4x + 2 4x

4x + 4

Step-by-step explanation:

F (x) = 2x - 1

G (x) = 3x + 2

H (x) = x²

We have to calculate the expression F (G (x)) - F (x)

F (G (x)) means the composition of functions F (x) and G (x). In order to find F (G (x)) we have to replace ever occurrence of x in F (x) with the value of G (x). So,

F (G (x)) = 2 (3x+2) - 1 = 6x + 4 - 1 = 6x + 3

Thus,

F (G (x)) - F (x) = 6x + 3 - (2x - 1)

= 6x + 3 - 2x + 1

= 4x + 4

Therefore, the expression F (G (x)) - F (x) equals 4x + 4