Question

Let f(x)=-6x+3 and g(x)=5x+4. Find f•g and state its domain

Answer 1

f(x)=-6x+3
f(-6)=(-6*-6)+3
f=-13/2

g(x)=5x+4
g(5)=25+4
g(5)=29
g=29/5

Ima let u solve the rest :D

Answer 2

`f\cdot g=-30x^2-9x+12`

Domain = All real numbers or (-∞,∞)

Explanation:

The given functions are

`f(x)=-6x+3`

`g(x)=5x+4`

We need to find the function f•g and its domain.

`f\cdot g=f(x)g(x)`

`f\cdot g=(-6x+3)(5x+4)`

`f\cdot g=-6x(5x+4)+3(5x+4)`

`f\cdot g=-6x(5x)-6x(4)+3(5x)+3(4)`

`f\cdot g=-30x^2-24x+15x+12`

`f\cdot g=-30x^2-9x+12`

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.