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From what I've gathered, I am unable to find the inverse function of the function shown here:

$$f(x) = \frac{-x \ln(|x - 1|) + \ln(|x - 1|) + x}{x^2}$$

The only part of the function $f$ that I have use for is when $x \le 1$, and a function fitting only this part should be able to be inverted. How can I find that?

If what I am asking is unclear: I primarily want to know how to invert the function $f$. If that is impossible, I want to find a very accurate approximate function so that I can invert that one instead.

Thanks for your time. :]

2012ssohn
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Valderhaug
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1 Answers1

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If we take a quick look at the graph, we can see that there are multiple values of $x$ where $f(x)=a$, $(\approx-0.224) < a < (\approx1.214)$. Graph of Function At $f(x)=0.1$, for example, $x$ could equal about 1.03 or 1.65.

Since this would mean the inverse would have multiple outputs at that location, it is impossible to find the inverse.

a52
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