Answer
a) $y=\dfrac{4x-8}{3}$; $f(x)=\dfrac{4x-8}{3}$
b) $f(3)=\dfrac{4}{3}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of equality to express the given equation, $
4x-3y=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}
4x-8=3y
\\\\
\dfrac{4x-8}{3}=\dfrac{3y}{3}
\\\\
y=\dfrac{4x-8}{3}
.\end{array}
Replacing $y$ with $f(x),$ the function notation form of the equation above is
\begin{array}{l}\require{cancel}
f(x)=\dfrac{4x-8}{3}
.\end{array}
Substituting $x=3,$ in the function above results to
\begin{array}{l}\require{cancel}
f(3)=\dfrac{4(3)-8}{3}
\\\\
f(3)=\dfrac{12-8}{3}
\\\\
f(3)=\dfrac{4}{3}
.\end{array}
