Answer:
[tex]f\cdot g=-30x^2-9x+12[/tex]
Domain = All real numbers or (-∞,∞)
Step-by-step explanation:
The given functions are
[tex]f(x)=-6x+3[/tex]
[tex]g(x)=5x+4[/tex]
We need to find the function f•g and its domain.
[tex]f\cdot g=f(x)g(x)[/tex]
[tex]f\cdot g=(-6x+3)(5x+4)[/tex]
[tex]f\cdot g=-6x(5x+4)+3(5x+4)[/tex]
[tex]f\cdot g=-6x(5x)-6x(4)+3(5x)+3(4)[/tex]
[tex]f\cdot g=-30x^2-24x+15x+12[/tex]
[tex]f\cdot g=-30x^2-9x+12[/tex]
It is a polynomial of degree 2. Domain of a polynomial function is all real number.
Therefore, the domain of f•g is all real numbers.
