Answer
$f(w) = \frac{4}{w^{2}}$
$w>0$
Work Step by Step
The volume formula is $V=lwh$.
We are told that the volume is $8ft^3$ and the length is twice the width so $l=2w$ and $V=8$.
Fill the known information into the volume formula $8=2w*w*h$
Multiply
$8=2{w^2}h$
Divide
$\frac{8}{2w^{2}} = \frac{2w^{2}h}{2w^{2}}$
Simplify $h = \frac{4}{w^{2}}$
$h=f(w)$
$f(w) = \frac{4}{w^{2}}$
Denominators can not be zero, so $w$ must be greater than zero.
$w>0$
