Question: Find the inverse of .
The first step is to switch x and y:
Then it's time for a little equation rearrangement:
Now I'm not sure how to proceed with this, but perhaps someone else can give a little insight.
I think, after thinking about it, that the correct solution is . My reasoning is that the original function is always above the line , so the inverse function must always be below the line . Note that the inverse is only defined for positive values of x, because the original function, which is also defined for only positive values of x, always produces positive outputs.