Plot for discrete set of data

Question

I was trying to make a plot of discrete set of data from two tables, the values in one table are fixed and the corresponding values in the other table are obtained from Mathematica itself by solving an equation using FindRoot command. I am having problems plotting the data from two tables. The code I wrote is as follows:

Table[x, {x, 0.1, 2, 0.1}]

y[_x] = Table[FindRoot[(Sqrt[1 + y[x]^2/x^2] +
    (y[x]/(2*x))^2*Log[(x/y[x])^2+Sqrt[1 + (x/y[x])^2]])*x/2 == 1, 
    {y[x], 1}], {x, 0.1, 2, 0.1}]
ListPlot[{y[x], x}]

The Problem being I am not getting the plot, it will be great if someone could help.Thanks.

Answer 1

xValues = Range[0.1, 2, 0.1];

yValues = y /. 
   Table[FindRoot[(Sqrt[1 + y^2/x^2] + (y/(2*x))^2*
          Log[(x/y)^2 + Sqrt[1 + (x/y)^2]])*x/2 == 1, {y, 1}], {x, 0.1, 2, 
     0.1}];

ListPlot with either

ListPlot[Transpose[{xValues, yValues}]]

ListPlot[yValues, DataRange -> {0.1, 2}]

Answer 2

I believe this is what you are seeking:

ListPlot[#[[1, 2]] & /@ 
  Table[FindRoot[(Sqrt[1 + z^2/x^2] + (z/(2*x))^2*
         Log[(x/z)^2 + Sqrt[1 + (x/z)^2]])*x/2 == 1, {z, 1.}], {x, 
    0.1, 2., 0.1}]]

If you have questions about syntax, feel free to comment upon this answer.