How to inverse the function $\frac13e^x+\ln(3x+1)$

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What would be the strategy and final result of inverting the function

$$f(x) = \frac{1}{3}e^x+\ln(3x+1)$$

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Almost impossible to find a nice formula, but simple to get a graph.

Once you have graphed $y=f(x)$ you simply draw the symmetric wrt the line $y=x$.

Hope this can be useful

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