## Intermediate Algebra (12th Edition)

$\text{a) } f(x)=3x^2+2 \\\\\text{b) } f(3)=29$
$\bf{\text{Solution Outline:}}$ Use the properties of equality to isolate $y$ in the given equation, $y-3x^2=2 ,$ 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} y-3x^2=2 \\\\ y=3x^2+2 .\end{array} Using $y=f(x),$ the function notation of the equation above is $f(x)=3x^2+2 .$ Substituting $x$ with $3 ,$ then \begin{array}{l}\require{cancel} f(x)=3x^2+2 \\\\ f(3)=3(3)^2+2 \\\\ f(3)=3(9)+2 \\\\ f(3)=27+2 \\\\ f(3)=29 .\end{array} Hence, \begin{array}{l}\require{cancel} \text{a) } f(x)=3x^2+2 \\\\\text{b) } f(3)=29 .\end{array}