Functions from the output of Solve

Question

The output of the equation

Solve[f[x] - x^2 == 0, f[x]]

is:

{{f[x] -> x^2}}

I would like the output to be

{f -> Function[x, x^2]}

In this way I can evaluate, for example,

f'[x] /. Out[2]

with the desired result,

2x

Can this be done? Of course I have many equations of this form, and far longer... Thanks, Max

Solve[f[x] - x^2 == 0, f[x]][[1]] /. Rule[func_, expr_] :> Rule[Head[func], (Function @@ {List @@ func, expr})] — Bob Hanlon, Commented May 7, 2023 at 17:36
There's an internal function that changes solutions to functions for DSolve: DSolve`DSolveToPureFunction[{{f[x] -> x^2}}] — Michael E2, Commented May 7, 2023 at 17:48

E. Chan-López · Accepted Answer · 2023-05-09 00:39:24Z

3

Use the resource function SolutionRulesToFunctions:

First@ResourceFunction["SolutionRulesToFunctions"][Solve[f[x] - x^2 == 0, f[x]]]

(*{f -> Function[{x}, x^2]}*)

answered May 8, 2023 at 14:59

E. Chan-López

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$\begingroup$ I did not know about the ResourceFunction site! Thanks, this is exactly what I was looking for. $\endgroup$
– MaxB
Commented May 8, 2023 at 22:56
$\begingroup$ I've added a hyperlink. Please see the update. :-) $\endgroup$
– E. Chan-López
Commented May 9, 2023 at 0:40

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