Question

What is the inverse of `y=3log(5x)+x^3`? ?

Answer 1

`x = 3log(5y)+y^3`

Explanation:

Given:

`y = 3log(5x)+x^3`

Note that this is only defined as a real valued function for `x > 0`.

Then it is continuous and strictly monotonically increasing.

The graph looks like this:
graph{y = 3log(5x)+x^3 [-10, 10, -5, 5]}

Therefore it does have an inverse function, whose graph is formed by reflecting about the `y=x` line...
graph{x = 3log(5y)+y^3 [-10, 10, -5, 5]}

This function is expressible by taking our original equation and swapping `x` and `y` to get:

`x = 3log(5y)+y^3`

If this were a simpler function then we would typically want to get this into the form `y = ...`, but that is not possible with the given function using standard functions.