# Tag Info

Accepted

### Why are there two inverses to exponentiation?

(Despite good answers already, I thought the concrete example below could be useful.) For multiplication and addition, there is exactly one inverse operation, namely division and subtraction. Yet ...
• 399
Accepted

### Apply the inverse operation on both sides, or know the inverse function?

I'd say both: they must know the inverse function, and that it's being applied to both sides. This then connects up with the fundamental properties of equality. As a teacher of many algebra courses (...
• 26.1k
Accepted

### What are some common ways students get confused about finding an inverse of a function?

I've noticed a few issues when students solve problems of the form, "Find the inverse of this function", and not all of the issues are necessarily because of the students' misunderstanding of what an ...
• 10.8k

### Why are there two inverses to exponentiation?

The other answers have shown that it depends on which of the two inputs you fix and which you let vary. As a way to visualize this, here's a plot of the 3D surface $z = x^y$. I've drawn two polynomial ...