#### Answer

$\text{a) }
f(x)=3x^2+2
\\\\\text{b) }
f(3)=29$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
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}