Plot a function with a recursion relation

Question

Consider the following functions:

r[x_] := r0 Exp[(k x)/(r1/(r1 + r[x]))];
f[x_] := (k x)/(r1/(r1 + r[x]));

and that

r1=1; r0=1; k=1;

I'd like to plot the function f[x]:

Plot[(k x)/(r1/(r1 + r[x])),{x,-1,1}]

How can the recursion relation can be dealt with?

Ruud3.1415 · Accepted Answer · 2018-01-22 13:31:10Z

4

For recursion relations we can use RSolve (this case can be solved algebraically however, see comments):

sol1 = RSolve[r[x] == r0 Exp[(k x)/(r1/(r1 + r[x]))], r[x], x]

to plot:

Plot[(k x)/(r1/(r1 + r[x])) /. sol1 /. {r1 -> 1, r0 -> 1, 
   k -> 1}, {x, -1, 1}]

answered Jan 22, 2018 at 13:20

Ruud3.1415

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$\begingroup$ You will however have this warning: Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. $\endgroup$
– Ruud3.1415
Commented Jan 22, 2018 at 13:22
1

$\begingroup$ And in this specific case, there is no need for recursion so sol2 = Solve[r[x] == r0 Exp[(k x)/(r1/(r1 + r[x]))], r[x]] will give you the exact same thing algebraically $\endgroup$
– Ruud3.1415
Commented Jan 22, 2018 at 13:28

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