I would like to plot the inverse of $f$ using the same method that was suggested to me in my previous question:

f(x_) := ((2 μ ArcTanh((# μ)/Sqrt(-α + #^2 ν)) + μ Log(α + #^2 (μ^2 – ν)) – 2 Sqrt(ν)Log(# ν + Sqrt(ν) Sqrt(-α + #^2 ν)))/( 2 μ^2 – 2 ν)) &(x) /. {μ -> 0.2, α -> 0.3, ν -> 0.5} // Abs;

ParametricPlot({{x, f(x)}, {f(x), x}}, {x, 0, 2})

But it’s not working?