The inverse of the exponential function

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Homework Help Overview

The discussion revolves around finding the inverse of the exponential function defined as f(x) = e^(x^3). Participants are exploring the relationship between exponential functions and their inverses, particularly focusing on the natural logarithm.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to find the inverse by suggesting ln(x^3) but expresses uncertainty about its correctness. Another participant suggests taking the natural logarithm of both sides to express x in terms of y. There is also a question about whether the resulting expression (ln x)^(1/3) is the correct inverse.

Discussion Status

The discussion is active, with participants providing different approaches to finding the inverse. Some guidance has been offered regarding the method of using logarithms, but there is no explicit consensus on the final form of the inverse function.

Contextual Notes

Participants are navigating through the definitions and properties of exponential and logarithmic functions, questioning assumptions about the inverse relationship. There may be confusion regarding the manipulation of expressions involving logarithms and exponents.

dalterego
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The inverse of the exponential function...

Homework Statement



Find the inverse of the function = e ^ (x^3)

Homework Equations



The inverse of the exponential function = the natural logarithm of that same function

The Attempt at a Solution



inverse of f(x) = ln(x^3) ?

This doesn't seem right.
 
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Nope. Let y=e^(x^3). Take Ln of both sides and express x in terms of y. Then replace y with x and you're done.
 


Alright, so is the answer

inverse of the function = (ln x)^1/3 ?
 


Yeah.
 

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