# Find the inverse of function h by a numerical way ?

Posted 18 days ago
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 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 complicatedBest regards,
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Posted 18 days ago
 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] *) 
Posted 17 days ago
 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?
Posted 18 days ago
 To obtain proper help, show the h function in code or attached a notebook.
Posted 17 days ago
 ok, I just edit my question.