Question

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

Answer 1

(a)

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)

Answer 2

The answer is A.
`30x^3-3x^2-24x+9`

Explanation:

In order to determine the final function, we need to know the meaning of

(f • g)(x). In math, when two function are being multiplied each other, the notation is:

f(x)•g(x)=(f • g)(x)

So, we have to multiply f(x) with g(x)

f(x)•g(x)=

`(5x^2+2x-3)*(6x-3)\\6x*(5x^2+2x-3)-3*(5x^2+2x-3)\\30x^3+12x^2-18x-15x^2-6x+9\\30x^3-3x^2-24x+9\\`

Finally the answer is:

(f • g)(x)=
`30x^3-3x^2-24x+9`

Other forms of notation in operations with functions:

f(x)+g(x)=(f+g)(x)

f(x)-g(x)=(f-g)(x)

`(f(x))/(f(y)) =((f)/(g))(x)`