Question

f(x) = 2x^3+4x^2+2x+1g(x) = x^3 –x^2+7x+9Find (f+g)(x):

Answer 1

Let's rewrite the functions:

$\begin{gathered} f(x)=2x^3+4x^2+2x+1 \\ g(x)=x^3-x^2+7x+9 \end{gathered}$

To get (f+g)(x), we just add them together:

$(f+g)(x)=f(x)+g(x)=2x^3+4x^2+2x+1+x^3-x^2+7x+9$

We can simplify be pairing the terms with the same order:

$\begin{gathered} (f+g)(x)=f(x)+g(x)=2x^3+x^3+4x^2-x^2+2x+7x+1+9= \\ =(2+1)x^3+(4-1)x^2+(2+7)x+10=3x^3+3x^2+9x+10 \end{gathered}$

So:

$(f+g)(x)=3x^3+3x^2+9x+10$