For this case we have the following functions:
[tex]f (x) = 3x + 1\\g (x) = x ^ 2-6[/tex]
We must find[tex](f-g) (x).[/tex]
By definition we have to:
[tex](f-g) (x) = f (x) -g (x)[/tex]
So:
[tex](f-g) (x) = 3x + 1- (x ^ 2-6)\\(f-g) (x) = 3x + 1-x ^ 2 + 6\\(f-g) (x) = - x ^ 2 + 3x + 6 + 1\\(f-g) (x) = - x ^ 2 + 3x + 7[/tex]
Answer:
[tex](f-g) (x) = - x ^ 2 + 3x + 7[/tex]
