#### Answer

(a) $f(x) = -\frac{x}{3}+4$
(b) $f(3) = 3$

#### Work Step by Step

(a) function notation.
Solve for $y$:
\begin{array}{ccc}
&x+3y&=&12
\\&x+3y-x &= &12-x
\\&3y&=&-x+12
\\&\frac{3y}{3} &= &\frac{-x+12}{3}
\\&y&=&-\frac{x}{3} + \frac{12}{3}
\\&y&=&-\frac{x}{3} + 4
\end{array}
Let $y=f(x)$. The equation becomes:
$$f(x)=-\frac{x}{3} + 4$$
(b) To find $f(3)$, substitute $3$ to $x$ in $f(x)$ to obtain:
$f(x)= -\frac{x}{3}+4
\\f(3) = -\frac{3}{3}+4
\\f(3)=-1+4
\\f(3)=3$