Final answer:
The question intends to find the inverse of a mathematical function but provides an unclear expression for y. A properly defined exponential function's inverse typically requires swapping variables and using logarithmic operations. However, without a clear function, it is not possible to find an inverse step-by-step.
Step-by-step explanation:
The subject of the question concerns finding the inverse function of a mathematical expression. To find the inverse, one typically swaps the x and y variables and then solves for y. It seems, however, that there may be a typo or some missing information in the student's provided function, as it is not presented in a clear mathematical form (y=(ʳ³⁸ ⁴/⁵). Assuming that the function is intended to represent an exponentiation or a root which often involves using the exponential function and its inverse, the natural logarithm (ln), we would proceed by taking the ln of both sides if the function were clearly stated.
As the question is currently unclear, we are unable to provide a step-by-step solution to find its inverse. A clearer question would involve a proper mathematical expression for y, after which we could find the inverse by applying the appropriate mathematical operations.