Answer
(a) $f(x)=\frac{x}{4}-2$
(b) $f(3)=-\frac{5}{4}$
Work Step by Step
(a) function notation.
Solve for $y$:
\begin{array}{ccc}
&x-4y&=&8
\\&x-4y-x &= &8-x
\\&-4y&=&-x+8
\\&\frac{-4y}{-4} &= &\frac{-x+8}{-4}
\\&y&=&\frac{-x}{-4} + \frac{8}{-4}
\\&y&=&\frac{x}{4} -2
\end{array}
Let $y=f(x)$. The equation becomes:
$$f(x)=\frac{x}{4} -2$$
(b) To find $f(3)$, substitute $3$ to $x$ in $f(x)$ to obtain:
$f(x)= \frac{x}{4}-2
\\f(3) = \frac{3}{4}-2
\\f(3)=\frac{3}{4}-\frac{8}{4}
\\f(3)=-\frac{5}{4}$
