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