p(x) = 2x^3 - 113 is shifted x^3.

    Therefore, it is one-to-one function over the entire domain  < x <  and maps the real number line by an one-to-one way onto itself.


To find the inverse function, express first x via p:

x = 


and then replace x by y and p by x. You will get the expression for the inverse function 

y = .     (1)


To calculate y(137), simply substitute 137 instead of x into the formula (1). You will get

y =  =  = 5.