Suppose that g(x) varies inversely with (x) and g(x) = 0.2 when x=0.1. what is g(x) when x=1.6?

Since g(x) varies with x, therefore:
g(x) = k/x where k is a constant.

So, first we need to get k. We are given that g(x) = 0.2 when x = 0.1
Substitute with these values to get k as follows:
g(x) = k/x
0.2 = k/0.1
k = 0.2*0.1 = 0.02

Now, the equation became:
g(x) = 0.02 / x

We need to get the g(x) when x = 1.6
Therefore, we will substitute with x in the equation and calculate the corresponding g as follows:
g(x) = 0.02 / 1.6
g(x) = 0.0125

0.0125  "Varies Inversely" means that when one of the items is multiplied by a constant, the other item is divided by the same constant. Or in mathematical notation. xy = k  So let's calculate k. xg(x) = k 0.1 * 0.2 = k 0.02 = k  
Therefore  
g(x) = 0.02/x 
 Let's plug in the value 1.6:
 g(1.6) = 0.02/1.6
 g(1.6) = 0.0125
 
 So our answer is 0.0125