Answer:
[tex]f * g = 21x ^ 2 + 32x +12[/tex]
Domain: all real numbers [tex](-\infty, \infty)[/tex]
Step-by-step explanation:
We have the functions [tex]f (x) = 3x + 2[/tex] and [tex]g (x) = 7x + 6[/tex]
We want to find f*g. Then we must multiply the function f by the function g.
Note that the function [tex]f (x) = 3x +2[/tex] is a linear function, therefore its domain is all real numbers. In the same way the function [tex]g (x) = 7x + 6[/tex] is also a linear function and its domain is all real numbers.
The multiplication of f * g will be
[tex]f * g = (3x + 2) (7x + 6)\\\\f * g = 21x ^ 2 + 18x + 14x +12\\\\f * g = 21x ^ 2 + 32x +12[/tex]
The function g(x) is a quadratic function and its domain is the intercept of the domain of f(x) with the domain of g(x), that is, all real numbers.
