Answer
(a) $f(x)=-2x^2-x+3$
(b) $f(3)=-18$
Work Step by Step
(a) function notation.
Solve for $y$:
\begin{array}{ccc}
&y+2x^2&=&3-x
\\&y+2x^2-2x^2&= &3-x-2x^2
\\&y&=&-2x^2-x+3
\end{array}
Let $y=f(x)$. The equation becomes:
$$f(x)=-2x^2-x+3$$
(b) To find $f(3)$, substitute $3$ to $x$ in $f(x)$ to obtain:
$f(x)= -2x^2-x+3
\\f(3) = -2(3^2)-3+3
\\f(3)=-2(9)-3+3
\\f(3)=-18-3+3
\\f(3)=-18$
