Answer
a) $f(x)+ g(x) = 3.6x+12.2$
b) $f(g(x))=-7x+25 $
c) $f(x)g(x)=-7x^2+3.4x+28.8 $
Work Step by Step
Given \begin{equation}
f(x)=5 x+9 \text { and } g(x)=-1.4 x+3.2
\end{equation} A) Add the two functions. \begin{equation}
\begin{aligned}
f(x)+g(x)& =5 x+9-1.4 x+3.2 \\
& = 3.6x+12.2.
\end{aligned}
\end{equation} Find $f(g(x))$.
\begin{equation}
\begin{aligned}
f(g(x))& = f(-1.4 x+3.2)\\
&=5 (-1.4 x+3.2)+9 \\
& = -7x+16+9\\
&= -7x+25.
\end{aligned}
\end{equation} C) Multiply the two functions.
\begin{equation}
\begin{aligned}
f(x)\cdot g(x)& =(5 x+9)\cdot(-1.4 x+3.2 )\\
& = -1.4x(5 x+9)+3.2(5 x+9)\\
& = -7x^2-12.6x+16x+28.8\\
& = -7x^2+3.4x+28.8.
\end{aligned}
\end{equation}
