Finding the inverse of two functions

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To find the inverse of the function y = e^(-x^3), a logical first step is to take the natural logarithm of both sides, leading to x = -ln(y)^(1/3). For the function y = sin(1/x), it is noted that the function is not invertible due to its many-to-one nature, as multiple x-values can yield the same y-value. Specifically, the sine function has infinitely many solutions for y = 0, which complicates finding a unique inverse. In general, to find an inverse, one must solve for x in terms of y and ensure the function is one-to-one over the desired domain. Understanding these steps is essential for successfully determining the inverses of these functions.
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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?
 
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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.
 
Tebow15 said:

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?
 

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