Given the functions:
[tex]\begin{gathered} f(x)=2x+1 \\ \\ g(x)=x^2-7 \end{gathered}[/tex]By definition, (f+g)(x) is equivalent to:
[tex](f+g)(x)=f(x)+g(x)[/tex]Finally, using the expressions for f and g:
[tex]\begin{gathered} f(x)+g(x)=2x+1+x^2-7 \\ \\ \therefore(f+g)(x)=x^2+2x-6 \end{gathered}[/tex]