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lmLtfy :p
\(\large f(x)=2x - \frac{3^x}{4}\) ??

Yes that's it

i don't think you can do it because as soon as you try to get that x out of the exponential, you lock the other x in a log
do you know if there is an answer and what that answer is? if so i can try to hack it or you can bump and wait for someone else to come along
to complicate matters, the other thing is this fails the so-called Horizontal Line Test - there is a local maximum, as you can see from the attached, so for f(x), 2 x's can map to the same y; but the inverse would require the opposite, ie that 1 y maps to 2 x's so there is no function
so that you would need to restrict the domain to the LHS or RHS of the turning point ....
not that helpful, i know :p

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