Answer
(a) $f(x) = \frac{4}{3}x-\frac{8}{3}$
(b) $f(3) = \frac{4}{3}$
Work Step by Step
(a) function notation.
Solve for $y$:
\begin{array}{ccc}
&4x-3y&=&8
\\&4x-3y-4x&= &8-4x
\\&-3y&=&-4x+8
\\&\frac{-3y}{-3}&=&\frac{-4x+8}{-3}
\\&y&=&\frac{4}{3}x-\frac{8}{3}
\end{array}
Let $y=f(x)$. The equation becomes:
$$f(x)=\frac{4}{3}x-\frac{8}{3}$$
(b) To find $f(3)$, substitute $3$ to $x$ in $f(x)$ to obtain:
$f(x)= \frac{4}{3}x-\frac{8}{3}
\\f(3) = \frac{4}{3}(3)-\frac{8}{3}
\\f(3)=4-\frac{8}{3}
\\f(3)=\frac{12}{3}-\frac{8}{3}
\\f(3)=\frac{4}{3}$