Find the intersection of two functions?

Questions
1

i can not find the intersection of two functions.
Intersections exist. You can see that when plotting the functions.
Please help me. I have added a screenshot and the Notebook file.

Code:

Clear[k, x, y, \[Phi], f1, f2, f3]

f1 = k*(x/(x + 1))*(x/(x + \[Phi]));

f2 = (k*x*(E^-x))*(x/(x + \[Phi]));

f3 = x;

k = 1.35;

\[Phi] = 0.01;

Plot[{f1, f2, f3}, {x, 0, 1}, 
 PlotLegends -> {BevertonHolt Wachstum, Ricker Wachstum, 
   Winkelhalbierende}]

Solve[f1 == f3, x]

Solve[f2 == f3, x]

question.jpg
question.jpg1920×1080 229 KB

question.nb (26.7 KB)

2

For most equations where the variable appears both as an argument to a transcendental function and elsewhere in the equation are not solvable in closed form.

intersection ver2.nb (48.9 KB)

3

thank you for your help.
I try to understand your solution. I am a beginner.