## Intermediate Algebra (12th Edition)

$\text{a) } f(x)=-2x^2+3 \\\\\text{b) } f(3)=-15$
$\bf{\text{Solution Outline:}}$ Use the properties of equality to isolate $y$ in the given equation, $y+2x^2=3 ,$ 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+2x^2=3 \\\\ y=-2x^2+3 .\end{array} Using $y=f(x),$ the function notation of the equation above is $f(x)=-2x^2+3 .$ Substituting $x$ with $3 ,$ then \begin{array}{l}\require{cancel} f(x)=-2x^2+3 \\\\ f(3)=-2(3)^2+3 \\\\ f(3)=-2(9)+3 \\\\ f(3)=-18+3 \\\\ f(3)=-15 .\end{array} Hence, \begin{array}{l}\require{cancel} \text{a) } f(x)=-2x^2+3 \\\\\text{b) } f(3)=-15 .\end{array}