Answer
a) $y=3x^2+x+2$; $f(x)=3x^2+x+2$
b) $f(3)=32$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of equality to express the given equation, $
y-3x^2=2+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=3x^2+x+2
.\end{array}
Replacing $y$ with $f(x),$ the function notation form of the equation above is
\begin{array}{l}\require{cancel}
f(x)=3x^2+x+2
.\end{array}
Substituting $x=3,$ in the function above results to
\begin{array}{l}\require{cancel}
f(3)=3(3)^2+3+2
\\\\
f(3)=3(9)+3+2
\\\\
f(3)=27+3+2
\\\\
f(3)=32
.\end{array}
