Answer :
Given:
The functions are:
[tex]f(x)=|3x-5|+7x[/tex]
[tex]g(x)=-2x+9[/tex]
To find:
The function [tex](f+g)(x)[/tex].
Solution:
We have,
[tex]f(x)=|3x-5|+7x[/tex]
[tex]g(x)=-2x+9[/tex]
We know that,
[tex](f+g)(x)=f(x)+g(x)[/tex]
On substituting the values of given functions, we get
[tex](f+g)(x)=|3x-5|+7x+(-2x+9)[/tex]
[tex](f+g)(x)=|3x-5|+7x-2x+9[/tex]
[tex](f+g)(x)=|3x-5|+5x+9[/tex]
Therefore, the required function is [tex](f+g)(x)=|3x-5|+5x+9[/tex].