Inverse of a function

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How can we find the inverse of $f(x) = 3x + e^{2x} $?

I am not able to separate the $x$ even taking the logarithm on both sides.

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It can't be expressed using elementary functions.

In future use Wolfram Alpha $$x = \frac16 \left(2y - 3W_n\left(\frac23e^{2y/3}\right)\right)$$