Answer
a) $y=\dfrac{x-8}{4}$; $f(x)=\dfrac{x-8}{4}$
b) $f(3)=-\dfrac{5}{4}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of equality to express the given equation, $
x-4y=8
,$ in terms of $y.$ Then replace $y$ with $f(x),$ to express the answer in function notation form. Finaly, substitute $x=3,$ to find $f(3).$
$\bf{\text{Solution Details:}}$
Using the properties of equality, the given equation is equivalent to
\begin{array}{l}\require{cancel}
x-8=4y
\\\\
\dfrac{x-8}{4}=\dfrac{4y}{4}
\\\\
y=\dfrac{x-8}{4}
.\end{array}
Replacing $y$ with $f(x),$ the function notation form of the equation above is
\begin{array}{l}\require{cancel}
f(x)=\dfrac{x-8}{4}
.\end{array}
Substituting $x=3,$ in the function above results to
\begin{array}{l}\require{cancel}
f(3)=\dfrac{3-8}{4}
\\\\
f(3)=\dfrac{-5}{4}
\\\\
f(3)=-\dfrac{5}{4}
.\end{array}
