# Finding the inverse of two functions

## Homework Statement

How do I find the inverse of these functions step by step?

y= e^-x^3

y= sin(1/x)

I know the solutions but I don't know how to work with these two functions. Does anyone know the steps to finding the inverse of these?

jbunniii
Homework Helper
Gold Member
The goal is to solve for x in terms of y.

What can you do to both sides of y = e^(-x^3) that would be a logical first step?

For the second function, y = sin(1/x), is there a restriction on the domain? As it's written, this function is not invertible because it's many-to-one. For example, there are infinitely many x for which sin(1/x) = 0, namely x = 1/(n*pi) for any nonzero integer n.

SammyS
Staff Emeritus
Homework Helper
Gold Member

## Homework Statement

How do I find the inverse of these functions step by step?

y= e^-x^3

y= sin(1/x)

I know the solutions but I don't know how to work with these two functions. Does anyone know the steps to finding the inverse of these?
How do you find the inverse of any function, in general?