Adding an empty circle to this plot, plus changing styles

Question

I cannot find a god solution to highlight the intersection point between these two curves, in the plot I made:

Clear[f, g, plot, reg];
f[x_] = Exp[x];
g[x_] = -x;
plot = Plot[{f[x], g[x]}, {x, -3, 3}, 
PlotStyle -> {Darker@Red, Darker@Gray}, AspectRatio -> Automatic, 
PlotLegends -> 
Placed[
 SwatchLegend[{Darker[Gray], 
   Darker[Red]}, {Style[Exp[x], Darker[Gray], Bold], 
   Style[Style[-x, Darker[Red], Bold]]}, 
  LegendMarkerSize -> {15, 15}], {0.2, 0.8}], 
AxesLabel -> {Style[x, Darker[Red]], Style[y, Darker[Red]]}];
Show[plot, PlotRange -> {-1, 4}, AxesStyle -> Arrowheads[{0.05}], 
 Axes -> True, Frame -> False, 
 GridLines -> {{{{Thick, AbsoluteDashing[{3, 3}]}}}, None}]

Here is what I would like to to, but I'm unable to.

• An empty circle, possibly in orange, around the intersection point between $e^x$ and $-x$.

• Making the axes bold (I tried with bold and thickness, it didn't work)

• Using a different font for axes label x and y

Anyway, more generally, I ask you: do you have some "good" improvement for this plot (or in general)?

I used to create plots with tikz, but I wanted to change a bit.

Thank you!

Answer 1

Clear[f, g, plot, reg];
f[x_] = Exp[x];
g[x_] = -x;
sol = {xx = SolveValues[f[x] == g[x], x][[1]], f[xx]} // Quiet;
plot = Plot[{f[x], g[x]}, {x, -3, 3},
   AxesStyle -> {Directive[Red], Bold},
   PlotStyle -> {Darker@Red, Darker@Gray}, AspectRatio -> Automatic, 
   PlotLegends -> 
    Placed[SwatchLegend[{Darker[Gray], 
       Darker[Red]}, {Style[Exp[x], Darker[Gray], Bold], 
       Style[Style[-x, Darker[Red], Bold]]}, 
      LegendMarkerSize -> {15, 15}], {0.2, 0.8}], 
   AxesLabel -> {Style[x, Darker[Red]], Style[y, Darker[Red]]},
   Epilog -> {Orange, Circle[sol, .3]}];
Show[plot, PlotRange -> {-1, 4},
 TicksStyle -> {{Red, 18, FontFamily -> "Times"}, {Blue, 24, 
    FontFamily -> "Courier"}},
 AxesStyle -> {{Thickness[0.01], 
    Arrowheads[{0.05}]}, {Thickness[0.01], Arrowheads[{0.05}]}}, 
 Axes -> True,
 Frame -> False, 
 GridLines -> {{{{Thick, AbsoluteDashing[{3, 3}]}}}, None}]