Find Inverse of f(x) = x+2e(x)

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To find the inverse of the function f(x) = x + 2e(x), the initial step involves switching y and x to get x = y + 2e(y). Attempts to isolate y using logarithmic properties and algebraic manipulation have proven unsuccessful. The user notes that there appears to be no straightforward algebraic method to solve for y in this equation. Suggestions for alternative approaches or insights into the problem are requested. The discussion highlights the complexity of finding the inverse for this specific function.
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Homework Statement



Let f(x)=x+2e(x). Find the inverse of f(x).

Homework Equations



e(a+b)=e(a)*e(b)
e(a-b)=e(a)/e(b)
ln(ab)=ln(a)+ln(b)
ln(a/b)=ln(a)-ln(b)
ln(a^b)=bln(a)

The Attempt at a Solution



Switch y and x so that
x=y+2e(y)
I tried applying ln to the functions at the start, subtracting y and then applying ln, applying ^2 to both sides but nothing seems to come of it. Any first suggestions?
 
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There is no "elementary algebra" way to solve that last equation for y.
 
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