Question

Given the following functions, find and simplify (f+g)(2).f(x) = 3x2+1g(x) = 3x−1Do not include "(f+g)(2) = " in your answer.

Answer 1

Given:

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

Therefore,

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

Let us now substitute x = 2

$\begin{gathered} (f+g)(2)=3(2)^2+3(2)=3(4)+6=12+6=18 \\ \therefore(f+g)(2)=18 \end{gathered}$

Hence,

$\begin{equation*} (f+g)(2)=18 \end{equation*}$