Given that f(x) = 5x^2 + 2x – 3, g(x) = 6x – 3, and h(x) = 2x + 9 find each function.
(f • g)(x)
a) 30x^3 – 3x^2 – 24x + 9
b) 15x^3 – 3x^2 – 24x + 9
c) 30x^3 + 24x^2 – 18x + 9
d) 15x^3 – 3x^2 + 24x – 9

(a)

Step-by-step explanation:

(f • g)(x) = f(x) × g(x), that is

(5x² + 2x - 3)(6x - 3)

Each term in the second factor is multiplied by each term in the forst factor, that is

5x²(6x - 3) + 2x(6x - 3) - 3(6x - 3) ← distribute all 3 parenthesis

= 30x³ - 15x² + 12x² - 6x - 18x + 9 ← collect like terms

= 30x³ - 3x² - 24x + 9 → (a)

twenty-six miles over two gallons because the proportion for the original 13 miles to one gallon would be written 13/1 and, doing the same thing to the top and bottom, i multiplied by 2 and got 26/2