The discussion centers on finding the inverse of the function f(x) = e^(x^2). The user correctly starts by reversing the variables to obtain x = e^(y^2) and then applies the natural logarithm to both sides, leading to ln(x) = y^2. However, the user incorrectly concludes with the expression [ln(y)]^(1/2), which does not logically follow from the previous step. The correct approach requires solving for y in terms of x, specifically y = sqrt(ln(x)).
PREREQUISITESStudents studying calculus, particularly those focusing on functions and their inverses, as well as educators looking for examples of function manipulation and inverse derivation.
well that last line does not follow from the one before it does it? You are trying to find y(x) remember.hahaha158 said:Homework Statement
##f(x)=e^{x^2}##
##f^{-1}(x)=?##2. The attempt at a solution
i reversed x and y so i got ##x=e^{y^2}##
ln both sides to get
##\ln|x|=y^2##
so ##[\ln|y|]^{1/2}##
what am i doing wrong?