For this case we have the following functions:
[tex]f (x) = 4x + 1\\g (x) = x ^ 2-5[/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) = 4x + 1- (x ^ 2-5)[/tex]
We take into account that:
[tex]- * + = -\\- * - = +\\(f-g) (x) = 4x + 1-x ^ 2 + 5\\(f-g) (x) = - x ^ 2 + 4x + 6[/tex]
Answer:
[tex](f-g) (x) = - x ^ 2 + 4x + 6[/tex]
Option C
