Answer
$\text{a) }
f(x)=\dfrac{-x+12}{3}
\\\\\text{b) }
f(3)=3$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of equality to isolate $y$ in the given equation, $
x+3y=12
,$ and then express in function notation. Then find $f(3)$ by substituting $x$ with $3.$
$\bf{\text{Solution Details:}}$
Using the properties of equality, the given equation is equivalent to
\begin{array}{l}\require{cancel}
x+3y=12
\\\\
3y=-x+12
\\\\
\dfrac{3y}{3}=\dfrac{-x+12}{3}
\\\\
y=\dfrac{-x+12}{3}
.\end{array}
Using $y=f(x),$ the function notation of the equation above is $
f(x)=\dfrac{-x+12}{3}
.$
Substituting $x$ with $
3
,$ then
\begin{array}{l}\require{cancel}
f(x)=\dfrac{-x+12}{3}
\\\\
f(3)=\dfrac{-3+12}{3}
\\\\
f(3)=\dfrac{9}{3}
\\\\
f(3)=3
.\end{array}
Hence,
\begin{array}{l}\require{cancel}
\text{a) }
f(x)=\dfrac{-x+12}{3}
\\\\\text{b) }
f(3)=3
.\end{array}