Let's rewrite the functions:
[tex]\begin{gathered} f(x)=2x^3+4x^2+2x+1 \\ g(x)=x^3-x^2+7x+9 \end{gathered}[/tex]To get (f+g)(x), we just add them together:
[tex](f+g)(x)=f(x)+g(x)=2x^3+4x^2+2x+1+x^3-x^2+7x+9[/tex]We can simplify be pairing the terms with the same order:
[tex]\begin{gathered} (f+g)(x)=f(x)+g(x)=2x^3+x^3+4x^2-x^2+2x+7x+1+9= \\ =(2+1)x^3+(4-1)x^2+(2+7)x+10=3x^3+3x^2+9x+10 \end{gathered}[/tex]So:
[tex](f+g)(x)=3x^3+3x^2+9x+10[/tex]