Question

First find f+g​, f−g​, f(g), and
`(f)/(g)`. Then determine the domain for each function.

Answer 1

I'll do f+g, you try the others on your own and comment if you need help with them! For f+g, you're just going to add the two functions together:


`f (x) = 3x + 7`


`g (x) = x + 9`


`(f +g)(x) = (3x + 7) + (x + 9) = 4x + 16`

Answer 2

`f(x) + g(x) = 3x + 2 + x + 6 = 4x + 8`. This function is defined for all real numbers.


`f(x) - g(x) = (3x + 2) - (x + 6) = 2x - 4`. This function is also defined for all real numbers.


`f(x) \cdot g(x) = (3x + 2) \cdot (x + 6) = 3x^2 + 2x + 18x + 12 = 3x^2 + 20x + 12.` As before, this function is defined for all real numbers
`x`.


`(f(x))/(g(x)) = (3x+2)/(x+6)`. Fractions are undefined when their denominators are zero, so if
`x + 6 = 0`, this function is undefined. Thus, the domain is all real numbers except
`x = -6`.