# Chapter 2 - Section 2.6 - Function Notation and Linear Functions - 2.6 Exercises: 47

$\text{a) } f(x)=\dfrac{-x+12}{3} \\\\\text{b) } f(3)=3$

#### 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}

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