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The known conditions are:

f[2 x + 1 _] = x^2 - 2 x

How to find the analytical formula f [x] of this function?

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    $\begingroup$ RSolve[f[2 x + 1 ] == x^2 - 2 x, f[x], x] ? $\endgroup$ Jun 4, 2023 at 12:48
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    $\begingroup$ Or by algebraic manipulation: Simplify /@ (f[2 x + 1] == x^2 - 2 x /. Solve[y == 2 x + 1, x][[1]]) /. {y -> x, Equal -> Rule} $\endgroup$
    – Bob Hanlon
    Jun 4, 2023 at 14:27

1 Answer 1

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Obtain answers based on Mariusz Iwaniuk prompts from netizens

RSolve[{f[2 x + 1] == x^2 - 2 x}, f[x], x] // Simplify // Expand
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