Question

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

Answer 1

`f(g(x))=-30x-21`

The domain is all real numbers

Explanation:

we have

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

`g(x)=5x+4`

we know that

`(fog)(x)=f(g(x))`

In the function f(x) substitute the variable x by the function g(x)

so

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

`f(g(x))=-30x-24+3`

`f(g(x))=-30x-21`

This is a linear function (equation of a line)

The domain is all real numbers