Question

Let f(x) = 3x + 2 and g(x) =7x + 6. Find f ·g and its domain.

Answer 1

`f * g = 21x ^ 2 + 32x +12`

Domain: all real numbers
`(-\infty, \infty)`

Explanation:

We have the functions
`f (x) = 3x + 2` and
`g (x) = 7x + 6`

We want to find f*g. Then we must multiply the function f by the function g.

Note that the function
`f (x) = 3x +2` is a linear function, therefore its domain is all real numbers. In the same way the function
`g (x) = 7x + 6` is also a linear function and its domain is all real numbers.

The multiplication of f * g will be

`f * g = (3x + 2) (7x + 6)\\\\f * g = 21x ^ 2 + 18x + 14x +12\\\\f * g = 21x ^ 2 + 32x +12`

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.