0
$\begingroup$

I want to plot f(x), inverse f(x) and f'(x) and then f(x)/f'(x) and inversef'(x)/inversef(x)

f[x_] := 2 a ArcTanh[(# a)/Sqrt[-1 + #^2 b]] + a Log[1 + #^2 (a^2 - b)] - 2 Log[# b + Sqrt[-1 + #^2 b]] &[x] /. {a -> 0.2, b -> 0.3};

I don't know from where I can start?

Improve this question
$\endgroup$
4
  • 1
    $\begingroup$ Your function f[x] is complex, is this feature intended? If yes your question cann#t be answered. $\endgroup$
    – Ulrich Neumann
    Dec 30, 2020 at 13:32
  • $\begingroup$ Yes but I like to know inverse f(x) and its differential and their plots mostly. $\endgroup$
    – Armin Sharafi
    Dec 30, 2020 at 13:35
  • $\begingroup$ Please clarify your question: You want to plot parts of a complex function: Re, Im, Abs,... $\endgroup$
    – Ulrich Neumann
    Dec 30, 2020 at 13:47
  • $\begingroup$ Abs I would like to know Abs $\endgroup$
    – Armin Sharafi
    Dec 30, 2020 at 13:49

2 Answers 2

Reset to default
2
$\begingroup$

To plot Abs[f[x]]==Sqrt[f[x] Conjugate[f[x]] try

f = 2 a ArcTanh[(# a)/Sqrt[-1 + #^2 b]] + a Log[1 + #^2 (a^2 - b)] -2 Log[# b + Sqrt[-1 + #^2 b]] & /. {a -> 2/10, b -> 3/10};
Plot[Sqrt[f[x] Conjugate[f[x]]] , {x, -5, 5} , PlotRange -> All]

enter image description here

The inverse function of Abs[f[x]] is only defined in subintervalls x<-2.17172,-2.17172<x<1.94146,x>1.94146.

Improve this answer
$\endgroup$
1
  • $\begingroup$ then I have this problem that how to introduce this f for plotting inversef'(x)/inversef(x) $\endgroup$
    – Armin Sharafi
    Dec 30, 2020 at 17:15
0
$\begingroup$ 
Clear["Global`*"]

f = 2 a ArcTanh[(# a)/Sqrt[-1 + #^2 b]] + a Log[1 + #^2 (a^2 - b)] - 
     2 Log[# b + Sqrt[-1 + #^2 b]] & /. {a -> 2/10, b -> 3/10};

Plot[Abs[f[x]], {x, -5, 5},
 PlotRange -> All,
 PlotPoints -> 100,
 MaxRecursion -> 10,
 AspectRatio -> 1,
 AxesLabel -> {"x", "|f(x)|"}]

enter image description here

Use ParametricPlot to plot the inverse

ParametricPlot[{Abs[f[x]], x}, {x, -5, 5},
 PlotRange -> All,
 PlotPoints -> 100,
 MaxRecursion -> 10,
 AspectRatio -> 1,
 AxesLabel -> {"|f(x)|", "x"}]

enter image description here

Use "Log" scaling (ScalingFunctions) for the derivative

Plot[Abs[f'[x]], {x, -5, 5},
 PlotRange -> All,
 PlotPoints -> 100,
 MaxRecursion -> 10,
 AspectRatio -> 1,
 AxesLabel -> {"x", "|f'(x)|"},
 ScalingFunctions -> "Log"]

enter image description here

as well as for the ratio

Plot[Abs[f[x]/f'[x]], {x, -5, 5},
 PlotRange -> All,
 PlotPoints -> 100,
 MaxRecursion -> 10,
 AspectRatio -> 1,
 AxesLabel -> {"x", "|f(x)/f'(x)|"},
 ScalingFunctions -> "Log"]

enter image description here

Improve this answer
$\endgroup$
2
  • $\begingroup$ for plotting inverse f'(x) / inverse f(x) ?? $\endgroup$
    – Armin Sharafi
    Dec 31, 2020 at 2:54
  • $\begingroup$ The inverses are not well-defined since they are multi-valued. You could use ParametricPlot to plot {Abs[f'[x]/f[x]], x} or {Log10[Abs[f'[x]/f[x]]], x} $\endgroup$
    – Bob Hanlon
    Dec 31, 2020 at 3:06

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.