Answer: The given statement is TRUE.
Step-by-step explanation: We are given the following two functions :
[tex]f(x)=3x+7,~~~\textup{and}~~~g(x)=5x-2.[/tex]
We are to check whether the following statement is true or false :
[tex](f+g)(x)=8x+5.[/tex]
We know that for any two functions p(x) and q(x), we have
[tex](p+q)(x)=p(x)+q(x).[/tex]
Therefore, we get
[tex](f+g)(x)\\\\=f(x)+g(x)\\\\=(3x+7)+(5x-2)\\\\=3x+7+5x-2\\\\=8x+5.[/tex]
Thus, [tex](f+g)(x)=8x+5.[/tex]
The given statement is TRUE.
