Answer
a) $y=-2x^2-x+3
$; $f(x)=-2x^2-x+3$
b) $f(3)=-18$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of equality to express the given equation, $
y+2x^2=3-x
,$ in terms of $y.$ Then replace $y$ with $f(x),$ to express the answer in function notation form. Finaly, substitute $x=3,$ to find $f(3).$
$\bf{\text{Solution Details:}}$
Using the properties of equality, the given equation is equivalent to
\begin{array}{l}\require{cancel}
y=-2x^2-x+3
.\end{array}
Replacing $y$ with $f(x),$ the function notation form of the equation above is
\begin{array}{l}\require{cancel}
f(x)=-2x^2-x+3
.\end{array}
Substituting $x=3,$ in the function above results to
\begin{array}{l}\require{cancel}
f(3)=-2(3)^2-(3)+3
\\\\
f(3)=-2(9)-3+3
\\\\
f(3)=-18-3+3
\\\\
f(3)=-18
.\end{array}