​ Function

What are you asking?   Is it a function?   

Here is a graph..... WHat do YOU think? Is it a function?

https://www.desmos.com/calculator/tcppo7vcvc

I do not know that I could simplify it further.....unless it is a sqrt rather than a cube root....

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See  EP's  answer  below

Welll...... if THAT is simplified, here is an easier way

mutiply by x/x

cube rt(4x/9x^3)    = cub rt 4x/9   / x      Multiply by 3/3

                              =    cub rt (12x/27) / x

                                 = 1/3x  cub rt 12x

                                  = \(\sqrt[3]{12x}\) / 3x                           Hmmmmmm....my answer is different than Chris'....will check