Respuesta :
Answer:
(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)
Answer:
The answer is A. [tex]30x^3-3x^2-24x+9[/tex]
Step-by-step 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)=
[tex](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\\[/tex]
Finally the answer is:
(f • g)(x)=[tex]30x^3-3x^2-24x+9[/tex]
Other forms of notation in operations with functions:
f(x)+g(x)=(f+g)(x)
f(x)-g(x)=(f-g)(x)
[tex]\frac{f(x)}{f(y)} =(\frac{f}{g})(x)[/tex]
