Find utility function given indifference curve? Given an indifference curve, how do you go about finding a utility function? 

For example, given $z= \frac{k^\frac{1}{\delta}}{x^\frac{\alpha}{\delta}y^\frac{\beta}{\delta}}$ (defined by $U(\cdot) = k$), find a utility function. To do this, would I have to assign an arbitrary number for the utility and rewrite the function? I'm confused about what to do and can't find anything in my textbook about it. Thanks
VCG's comment about isolating $k$ is the correct approach.

Given $U(\cdot) = k$ and
$$z = \frac{k^\frac{1}{\delta}}{x^\frac{\alpha}{\delta}y^\frac{\beta}{\delta}}$$
raise each side to the $\delta$ power:
$$z^\delta = \frac{k}{x^\alpha y^\beta}$$
and isolate $k$
$$k = x^\alpha y^\beta z^\delta$$

Since $k$ is now a function of each of the goods in your equation, it makes sense as a function form for utility.

$$U(x, y, z) = x^\alpha y^\beta z^\delta$$
So we arrive at the Cobb-Douglass utility form.