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Can I use inverse of the same function when defining the function itself? For example 

b[x_]:=1+Integrate[InverseFunction[b][a],{a,0,x}]
b[5]

Typing that in I get an error:

$RecursionLimit::reclim: Recursion depth of 256 exceeded.

A simpler example:

b[x_] := 1 + InverseFunction[b][x]
b[5]

also gives me the same error.

I understand that it has to do with the fact that a function has its own inverse in its definition, which is not easy to solve (maybe not possible?)

Could you please give me some advice on what to do in the case that I want to solve a problem of this type (my actual problem is more complicated, but I wanted to know on the simpler example).

Are there any other ways to get a solution for this type of problem?

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因此，您不能在函数定义期间引用逆。人们可以很容易地构建这样一个定义不明确的情况。您可以做的是分析您的函数以提出等效的显式描述。在你的第二个例子中，函数

b[x_] := 1/2 + x

会满足条件。我发现通过在图表中可视化函数，x轴上的参数和y上的结果。然后取反对应于行x=y中的反射。因此，如果某个点(x,y)属于您的函数，那么(y,x+1)也是如此。重复执行此操作，您会很好地了解函数的外观，至少如果您假设它是连续的。

对于积分的第一个示例，事情会更加困难，但是如果您在那里需要帮助，最好在Math Stack Exchange询问，因为这不是关于如何使用 Mathematica。

于 2014-06-16T19:03:03.887 回答