The function for the cost of materials to make a hat is f (x) = one half x + 1, where x is the number of hats. The function for the selling price of those hats is g (f (x)), where g (x) = x + 2. Find the selling price of 10 hats.

Here we're dealing with a "composite function," where the input to one function (g) is another function (f).

Given that g (x) = x + 2. We need to find the value of this function when the input is the other function: f (x) = (1/2) x + 1. Making these substitutions, we get g (f (x)) = [ (1/2) x + 1] + 2.

The selling price of 10 hats is now found by replacing x with 10:

g (f (10)) = [ (1/2) {10} + 1] + 2

= [5+1] + 2 = 6 + 2 = 8 cost units (answer)