Wolfram alpha gives incorrect inverse function

Question

I have trouble with Wolfram Alpha not fully calculating inverse of higher-order polynomial function. Function $$f(x)=3 x^6-5 x^4-4 x^2+8$$ (graph presented on a first photo Graph of $f(x)$) is not a one-to-one function. Was one to calculate its inverse the result would be either four different functions or $\pm$ sign which would result in the function having four different inverses for different domains of $x$, where $f(x)$ is one-to-one. Such answer is also given by wolfram inverese of the function according to wolfram, however, after copying the anser into geogebra the resulting graph is different from the plot given by wolfram Graph of function given by wolfram, as seemingly two parts are missing, which is especially visible after comparing $f(x)$ and $f^{-1}(x)$ on the same graph Final wolfram's answer and starting $f(x)$. Is there some way to find the functions describing the middle part of the graph $f(x)$? Wolfram does realise the $4$ functions problem for simpler functions such as inverse of $$4 x^4-10 x^2+8$$ as it is able to give two distinct functions starting with $\pm$ as a result. Inverse of simple function which would also be one-to-four Thank you in advance