Intermediate Algebra (12th Edition)

$\text{a) } f(x)=\dfrac{4}{3}x-\dfrac{8}{3} \\\\\text{b) } f(3)=\dfrac{4}{3}$
$\bf{\text{Solution Outline:}}$ 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}