Answer:
[tex](f-g)(x)[/tex][tex]=6[/tex]
Step-by-step explanation:
Given:
[tex]f(x)=x+3\\g(x)=x-3[/tex]
To find [tex](f-g)(x)[/tex]
Solution:
In order to find [tex](f-g)(x)[/tex] we will subtract the function [tex]g(x)[/tex] from [tex]f(x)[/tex]
So, we have:
[tex](f-g)(x)[/tex][tex]=f(x)-g(x)[/tex]
Plugging in [tex]f(x)[/tex] and [tex]g(x)[/tex] in the above combinations of functions.
[tex](f-g)(x)[/tex][tex]=(x+3)-(x-3)[/tex]
Simplifying by removing the parenthesis and reversing the signs of the terms in the parenthesis after the negative.
[tex](f-g)(x)[/tex][tex]=x+3-x+3[/tex]
Combining like terms.
[tex](f-g)(x)[/tex][tex]=x-x+3+3[/tex]
∴ [tex](f-g)(x)[/tex][tex]=6[/tex]
