Answer
a) $f(x)+ g(x) = 2 x^2+9 x-13$
b) $f(g(x))=8 x^2-26 x+7 $
c) $f(x)g(x)= 4x^3+4x^2-51x+40 $
Work Step by Step
Given \begin{equation}
f(x)=2 x^2+7 x-8 \text { and } g(x)=2 x-5.
\end{equation} A) Add the two functions.
\begin{equation}
\begin{aligned}
f(x)+g(x)& =2 x^2+7 x-8+2 x-5 \\
&=2 x^2+9 x-13.
\end{aligned}
\end{equation} B) Find $f(g(x))= f(2 x-5)$.
\begin{equation}
\begin{aligned}
f(g(x))& =2(2 x-5)^2+7(2 x-5)-8 \\
& = 2(4x^2-20x+25)+14x-35-8\\
& =8 x^2-40 x+14 x+50-43\\
&=8 x^2-26 x+7.
\end{aligned}
\end{equation} C) Multiply the two functions.
\begin{equation}
\begin{aligned}
f(x)\cdot g(x)& =(2 x^2+7 x-8)\cdot(2 x-5 )\\
& = 2x^2(2 x-5 )+7x(2 x-5 )-8(2 x-5 )\\
& = 4x^3-10x^2+14x^2-35x-16x+40\\
& = 4x^3+4x^2-51x+40.
\end{aligned}
\end{equation}
