Answer
$\text{a) }
f(x)=-2x^2+3
\\\\\text{b) }
f(3)=-15$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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}
