Calculus Problem, Finding the Inverse of a function

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SUMMARY

The discussion focuses on finding the inverse of the function f(x) = sqrt(ln(x)). The correct inverse is established as f_inv(x) = exp(x^2). Participants confirm the validity of the solution by verifying that f_inv(f(x)) = f(f_inv(x)) = x. A crucial point raised is the importance of using consistent variable notation, specifically advising against mixing variables such as t and x in the context of function definitions.

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  • Ability to manipulate algebraic expressions
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Homework Statement



http://img17.imageshack.us/img17/4413/asasasasas.jpg

Homework Equations


let t = e^x.


The Attempt at a Solution




f(x) = sqrt(ln(x))

f_inv(x) = exp(x^2)


is that it? Nothing more to it?
 
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I don't see anything wrong with your work. You can check to see that f-1(f(x)) = f(f-1(x)) = x.
 
I wish you would NOT say "let t= e^x" and then write "f(x)= sqrt(ln(x))" when you mean "f(t)= sqrt(ln(t))"!
 

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