Keywords:
Functions, subtraction, operation of functions
For this case, we are given two functions of the form [tex]y_ {1} = f (x)[/tex], where [tex]f (x) = 4x + 1[/tex] and[tex]y_ {2} = g (x)[/tex], where [tex]g (x) = x ^ 2-5[/tex]. We must find the subtraction (f-g) (x). So, by definition of operation of functions we have to:
[tex](f-g) (x) = f (x) -g (x)[/tex]
So, we have:
[tex](f-g) (x) = 4x + 1- (x ^ 2-5)[/tex]
Knowing that: [tex]- * + = -\ and\ - * - = +[/tex]
[tex](f-g) (x) = 4x + 1-x ^ 2 + 5\\(f-g) (x) = - x ^ 2 + 4x + 6[/tex]
Answer:
[tex](f-g) (x)[/tex]is given by[tex]-x ^ 2 + 4x + 6[/tex]
