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

##### 1 Answer

Oct 1, 2017

#### Explanation:

Given:

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

Note that this is only defined as a real valued function for

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

graph{x = 3log(5y)+y^3 [-10, 10, -5, 5]}

This function is expressible by taking our original equation and swapping

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

If this were a simpler function then we would typically want to get this into the form