Find the inverse of function h by a numerical way ?

Questions
1

Hello guys, Please I have a question: I need to know the inverse of function “h= a + Q” defined as follows:

(*Définit la fonction indicatrice*)
indicator[x_] := Piecewise[{{1, 0 < x < \[Pi]/2}}, 0];
(*Semi groupe*)
S[x_, t_] := Sum[ Exp[- t  n^2] Integrate[x Sin[s n^2], {s, 0, \[Pi]}]  Sin[x n^2], {n, 5}]
(*controllability map*)
G[x_, t_] := indicator[x] S[x, T - t]
(*Grammian operator Q*)
Q[x_, t_] := (indicator[x])^2  Integrate[(S[x, T - s])^2, {s, T - l, T}]
v[x_, t_] := InverseFunction[a + Q][x, t];
(*Test*)
N[v[w1 - S[1, T], T] ]

It’s not working for me because of the expression of “h=a + Q” which is complicated

Best regards,

2

You can try something like this as long as h has a single value in the inverse domain.

Using Sin as an example

data = Table[{N@Sin[x], x}, {x, 0, Pi/2, Pi/200}];
invF = Interpolation[data];

invF[1/Sqrt[2]] / Degree
(* 45. *)

Sin[45 Degree]
(* 1/Sqrt[2] *)
3

To obtain proper help, show the h function in code or attached a notebook.

4

Hi Rohit, I just edit my question, I specified the expression of the function to inverse!
Do you have any idea why it’s not working pleas?

5

ok, I just edit my question.

6

This seems to be the same question as this .

7

Indeed yes, I have just checked it is my partner in this work who asked the question, I will send him a message so that he deletes this message not to repeat the same question.